Question

The perimeter of a rectangular atrium is 220 inches. The length of the atrium is four times the width. Find the length and the width.

Answer 1

Answer: Width of atrium = 22 inches

Length of atrium = 88 inches.

Explanation:

Given : The length of the atrium is four times the width.

Let w be the width of atrium , then its length will be l= 4w.

Formula to find perimeter:-

`P=2(l+w)`

`P=2(4w+w)=2(5w)=10w`

Since, The perimeter of a rectangular atrium is 220 inches.

Then, we have

`10w=220\\\\\Rightarrow\ w=(220)/(10)=22`

Width of atrium = 22 inches

Length of atrium = 4(22)=88 inches.

Answer 2

The length of the rectangular atrium is 88 inches and the width is 22 inches

Explanation:

Let

x ----> the length of the rectangular atrium

y ----> the width of the rectangular atrium

we know that

The perimeter of the rectangular atrium is

`P=2(x+y)`

`P=220\ in`

so

`220=2(x+y)`

Simplify

`110=(x+y)` ----> equation A

`x=4y` -----> equation B

substitute equation B in equation A and solve for y

`110=(4y+y)`

`110=5y`

Divide by 5 both sides

`y=22\ in`

Find the value of x

`x=4(22)=88\ in`

therefore

The length of the rectangular atrium is 88 inches and the width is 22 inches