Question

||

Finding the dimensions of a rectangle given its perimeter and a...
The length of a rectangle is five times its width.
If the perimeter of the rectangle is 120 in, find its length and width.
length: 111
width: in
X
E
S

Answer 1

Width = 10 in

Length = 50 in

Explanation:

Define the variables

• Let x be the width of the rectangle.

• If the length is five times its width, then the length of the rectangle is 5x.

Given the perimeter is 120 in:

`\begin{aligned}\textsf{Perimeter of a rectangle} & = 2(\sf width + length)\\120 & = 2(x + 5x)\\120 & = 2(6x)\\120 & = 12x\\(12x)/(12)&=(120)/(12)\\\implies x&=10\end{aligned}`

Solution:

• Width = 10 in
• Length = 5 × 10 in = 50 in