# geometry

The perimeter of an isosceles triangle is 42 cm . its base is 2/3 times the sum of the equal sides . find the length of each side and the area of the triangle.

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1. 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
multipy 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

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2. the perimeter of an isosceles triangle is 42cm and its bases is(3/2) times each of the equal sides .find the length of each side of the triangle ;area of the triangle and the height of the triangle.

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