Question

A square and a rectangle have the same perimeter. The square has a side length of 8x units. The rectangle has a length of (5x+8) units and a width of 14 units. What will the perimeter of both the rectangle and the square

Answer 1

The perimeter of both figures is equal to
`64\ units`

Explanation:

step 1

we know that

The perimeter of a square is equal to

`P=4b`

where

b is the side length of the square

we have

`b=8x\ units`

substitute

`P=4(8x)=32x\ units`

step 2

we know that

The perimeter of a rectangle is equal to

`P=2(L+W)`

we have

`L=(5x+8)\ units`

`W=(14)\ units`

substitute

`P=2(5x+8+14)=10x+44\ units`

step 3

Equate both perimeters and solve for x

`10x+44=32x`

`32x-10x=44`

`22x=44`

`x=2\ units`

step 4

Find the perimeter of both

square

`P=32x=32(2)=64\ units`

rectangle

`P=10x+44=10(2)+44=64\ units`