Question

If the area of a square with side x is equal to the area of a triangle with base x, then find the altitude of the triangle.

Answer 1

`h= 2x`

Explanation:

Given

Square

`Side = x`

Triangle

`Base = x`

`Altitude = h`

Required

Find h, if both shapes have the same area

The area of the square is:

`Area = x * x`

`Area = x^2`

The area of the triangle is:

`Area = (1)/(2) * Base*Height`

`Area = (1)/(2) * x*h`

Equate both areas

`x^2 = (1)/(2) * x*h`

Divide both sides by x

`x = (1)/(2) *h`

Multiply both sides by 2

`2*x = (1)/(2) *h*2`

`2x = h`

`h= 2x`