Which of the following can be the third side of a triangle whose two sides are 7cm and 9cm
RS Aggarwal Solutions Class 9 Mathematics Solutions for Congruence Of Triangles And Inequalities In A Triangle Exercise 9B in Chapter 9 - Congruence Of Triangles And Inequalities In A TriangleQuestion 1 Congruence Of Triangles And Inequalities In A Triangle Exercise 9B Show
Is it possible to construct a triangle with lengths of its sides as given below? Give reason for your answer. (i) 5cm, 4cm, 9cm (ii) 8cm, 7cm, 4cm (iii) 10cm, 5cm, 6cm (iv) 2.5cm, 5cm, 7cm (v) 3cm, 4cm, 8cm Answer: (i) No. It is not possible to construct a triangle with lengths of its sides 5cm, 4cm and 9cm because the sum of two sides is not greater than the third side i.e. 5 + 4 is not greater than 9. (ii) Yes. It is possible to construct a triangle with lengths of its sides 8cm, 7cm and 4cm because the sum of two sides of a triangle is greater than the third side. (iii) Yes. It is possible to construct a triangle with lengths of its sides 10cm, 5cm and 6cm because the sum of two sides of a triangle is greater than the third side. (iv) Yes. It is possible to construct a triangle with lengths of its sides 2.5cm, 5cm and 7cm because the sum of two sides of a triangle is greater than the third side. (v) No. It is not possible to construct a triangle with lengths of its sides 3cm, 4cm and 8cm because the sum of two sides is not greater than the third side.
Was This helpful?  Q12) Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is the third side? Let the length of the third side be x cm. The length of the other two sides is 12 cm and 14 cm. Thus, the length of third side is 10 cm. Hello students, welcome to the Lido learning. So here the question is two supplementary angles are Phi x minus 82 degrees + 4 x + 73 degrees. So here we have to find the value of the X. So let us write it starts the answer. So here solution is supplementary angles are 180 degrees, right? So here the equation is 5X minus 82 degrees plus 44 x + 73 degrees is 180 degrees. So you're freaking observe 9x minus 9 9 x minus 9 is equal to 180 degrees. So 9 x if we sent to the right-hand side we get 9x is equals to 1 89. So here if we send mine from multiplying to the right-hand side dividing. Sorry. Sorry. Sorry dividing X equals to one eighty-nine by nine is equal to the answer the final answer we get the x value is 21 degrees. Thank you for watching our video. A subscriber to our Channel and feel free to ask doubts in the comment section below. Thank you. The area of an isosceles triangle is the amount of region enclosed by it in a two-dimensional space. The general formula for the area of triangle is equal to half the product of the base and height of the triangle. Here, a detailed explanation of the isosceles triangle area, its formula and derivation are given along with a few solved example questions to make it easier to have a deeper understanding of this concept. Check more mathematics formulas here. What is the Formula for Area of Isosceles Triangle?The total area covered by an isosceles triangle is known as its area. For an isosceles triangle, the area can be easily calculated if the height (i.e. the altitude) and the base are known. Multiplying the height with the base and dividing it by 2, results in the area of the isosceles triangle. What is an isosceles triangle? An isosceles triangle is a triangle that has any of its two sides equal in length. This property is equivalent to two angles of the triangle being equal. An isosceles triangle has two equal sides and two equal angles. The name derives from the Greek iso (same) and Skelos (leg). An equilateral triangle is a special case of the isosceles triangle, where all three sides and angles of the triangle are equal. An isosceles triangle has two equal side lengths and two equal angles, the corners at which these sides meet the third side is symmetrical in shape. If a perpendicular line is drawn from the point of intersection of two equal sides to the base of the unequal side, then two right-angle triangles are generated. Table of Contents:
The area of an isosceles triangle is given by the following formula: Also,
List of Formulas to Find Isosceles Triangle Area
How to Calculate Area if Only Sides of an Isosceles Triangle are Known?If the length of the equal sides and the length of the base of an isosceles triangle are known, then the height or altitude of the triangle is to be calculated using the following formula: Altitude of an Isosceles Triangle = √(a2 − b2/4) Thus, Area of Isosceles Triangle Using Only Sides = ½[√(a2 − b2 /4) × b] Here,
Derivation for Isosceles Triangle Area Using Heron’s FormulaThe area of an isosceles triangle can be easily derived using Heron’s formula as explained below. According to Heron’s formula, Area = √[s(s−a)(s−b)(s−c)] Where, s = ½(a + b + c) Now, for an isosceles triangle, s = ½(a + a + b) ⇒ s = ½(2a + b) Or, s = a + (b/2) Now, Area = √[s(s−a)(s−b)(s−c)] Or, Area = √[s (s−a)2 (s−b)] ⇒ Area = (s−a) × √[s (s−b)] Substituting the value of “s” ⇒ Area = (a + b/2 − a) × √[(a + b/2) × ((a + b/2) − b)] ⇒ Area = b/2 × √[(a + b/2) × (a − b/2)] Or, area of isosceles triangle = b/2 × √(a2 −
b2/4) Area of Isosceles Right Triangle FormulaThe formula for Isosceles Right Triangle Area= ½ × a2 Derivation: Area = ½ ×base × height area = ½ × a × a = a2/2 Perimeter of Isosceles Right Triangle FormulaDerivation: The perimeter of an isosceles right triangle is the sum of all the sides of an isosceles right triangle. Suppose the two equal sides are a. Using Pythagoras theorem the unequal side is found to be a√2. Hence, perimeter of isosceles right triangle = a+a+a√2 = 2a+a√2 = a(2+√2) = a(2+√2) Area of Isosceles Triangle Using TrigonometryUsing Length of 2 Sides and Angle Between Them A = ½ × b × c × sin(α) Using 2 Angles and Length Between Them A = [c2×sin(β)×sin(α)/ 2×sin(2π−α−β)] Solved ExamplesExample 1: Find the area of an isosceles triangle given b = 12 cm and h = 17 cm? Base of the triangle (b) = 12 cm Height of the triangle (h) = 17 cm Area of Isosceles Triangle = (1/2) × b × h = (1/2) × 12 × 17 = 6 × 17 = 102 cm2 Example 2: Find the length of the base of an isosceles triangle whose area is 243 cm2, and the altitude of the triangle is 27 cm. Solution: Area of the triangle = A = 243 cm2 Height of the triangle (h) = 27 cm The base of the triangle = b =? Area of Isosceles Triangle = (1/2) × b × h 243 = (1/2) × b × 27 243 = (b×27)/2 b = (243×2)/27 b = 18 cm Thus, the base of the triangle is 18 cm. Question 3: Find the area, altitude and perimeter of an isosceles triangle given a = 5 cm (length of two equal sides), b = 9 cm (base). Solution: Given, a = 5 cm b = 9 cm Perimeter of an isosceles triangle = 2a + b = 2(5) + 9 cm = 10 + 9 cm = 19 cm Altitude of an isosceles triangle h = √(a2 − b2/4) = √(52 − 92/4) = √(25 − 81/4) cm = √(25–81/4) cm = √(25−20.25) cm = √4.75 cm h = 2.179 cm Area of an isosceles triangle = (b×h)/2 = (9×2.179)/2 cm² = 19.611/2 cm² A = 9.81 cm² Question 4: Find the area, altitude and perimeter of an isosceles triangle given a = 12 cm, b = 7 cm. Solution: Given, a = 12 cm b = 7 cm Perimeter of an isosceles triangle = 2a + b = 2(12) + 7 cm = 24 + 7 cm P = 31 cm Altitude of an isosceles triangle = √(a2 − b2⁄4) = √(122−72/4) cm = √(144−49/4) cm = √(144−12.25) cm = √131.75 cm h = 11.478 cm Area of an isosceles triangle = (b×h)/2 = (7×11.478)/2 cm² = 80.346/2 cm² = 40.173 cm² Practice Questions
Frequently Asked Questions on Area of Isosceles TriangleWhat is an Isosceles Triangle?An isosceles triangle can be defined as a special type of triangle whose 2 sides are equal in measure. For an isosceles triangle, along with two sides, two angles are also equal in measure. What does the Area of an Isosceles Triangle Mean?The area of an isosceles triangle is defined as the amount of space occupied by the isosceles triangle in the two-dimensional plane. What is the Formula for Area of Isosceles Triangle?To calculate the area of an isosceles triangle, the following formula is used: A = ½ × b × h What is the Formula for Perimeter of Isosceles Triangle?The formula to calculate the perimeter of an isosceles triangle is: P = 2a + b So, the length of the third side must lie between 2 cm and 16 cm. Thus, 3 cm < third side <17 cm. In given options, only option 3 i.e. 4 cm lies in between required range. The SSC CGL 2022 Amendment Notice Out on 30th September 2022. (Perpendicular)2 + (Base)2 = (Hypotenuse)2 Using the above equation third side can be calculated if two sides are known. Which of the following can be the third side of triangle if two sides are 9cm 6cm?We know that, The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. The difference in the lengths of any two sides of a triangle is always smaller than the length of the third side. Therefore, 5 cm is the length of the 3rd side.
How do you find a third side of a triangle given two sides?Finding Third Side of a Triangle given Two Sides
According to Pythagoras Theorem, the sum of squares of two sides is equal to the square of the third side.
Which of the following can be the third side of a triangle whose two sides are 7 cm and 10cm respectively?Thus, 3 cm < third side <17 cm.
Which of the following can be the third side of a triangle whose two sides are 8cm and 5cm respectively?Therefore, the third side of a triangle can be 5cm. Was this answer helpful?
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