Question

The perimeter of an isosceles triangle is 42 cm. Its base is 2/3 times the sum of equal sides. Find the length of each side of the triangle.​

Answer 1

Answer:

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Step-by-step explanation:

let each of the equal sides be x  

let the base by y  

y = (2/3)(2x) = 4x/3  

so x + x + (4/3)x = 42  

multiply by 3  

3x + 3x + 4x = 126  

10x = 126  

x = 12.6  

so the base = (4/3)(12.6) = 16.8  

use Pythagoras to find the height, h  

h^2 + 8.4^2 = 12.6^  

h^2 = 88.2  

h √88.2  

Area = (1/2)base x height  

= (1/2)(16.8)√88.2  

= appr. 78.888

Answer 2

Step-by-step explanation:

Sum of equal sides = x

Its base =2/3x

x+2x/3=42

x+2x=42× 3

x+2x=126

3x=126

x=126/3

x=42

It's base = 2/3×42 = 28

Equal sides = 42/2 = 21

Hence three sides of an isosceles triangles are 21cm,21 cm, 28cm

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