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

Answer:

$h= 2x$

Step-by-step 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:

$Area = \frac{1}{2} * Base*Height$

$Area = \frac{1}{2} * x*h$

Equate both areas

$x^2 = \frac{1}{2} * x*h$

Divide both sides by x

$x = \frac{1}{2} *h$

Multiply both sides by 2

$2*x = \frac{1}{2} *h*2$

$2x = h$

$h= 2x$