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.

Step-by-step 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

$10w=220\\\\\Rightarrow\ w=\dfrac{220}{10}=22$

Width of atrium = 22 inches

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

Answer 2

Answer:

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

Step-by-step 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