Question

A rectangle and a triangle have the same area, 72 . The height of the triangle is also the same as the width of the rectangle. The base of the triangle is 18 in., and the length of the rectangle is 9 in. Find the missing dimension.

Answer 1

Part 1) The height of triangle is
`h=8\ in`

Part 2) The width of rectangle is
`W=8\ in`

Explanation:

step 1

Find the dimensions of triangle

The area of triangle is equal to

`A=(1)/(2)bh`

we have

`b=18\ in`

`A=72\ in^(2)`

substitute and solve for h

`72=(1)/(2)(18)h`

`144=(18)h`

`h=144/18=8\ in`

step 2

Find the missing dimension of rectangle

we have that

The height of the triangle is the same as the width of the rectangle

therefore

`W=h=8\ in`