Question

linear equations
finding the dimensions of a rectangle given its perimeter and a...
the length of a rectangle is twice its width.
if the perimeter of the rectangle is 54 yd, find its length and width.
length: yd
width: yd

Explanation:

Step1: Set up variables

Let the width of the rectangle be \( w \) yd. Then the length \( l = 2w \) yd.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P=2(l + w) \). Substitute \( l = 2w \) and \( P = 54 \) into the formula: \( 54=2(2w+w) \).
Simplify the right - hand side: \( 54 = 2\times3w\), so \( 54=6w \).

Step3: Solve for \( w \)

Divide both sides of the equation \( 54 = 6w \) by 6: \( w=\frac{54}{6}=9 \) yd.

Step4: Solve for \( l \)

Since \( l = 2w \), substitute \( w = 9 \) into the equation: \( l=2\times9 = 18 \) yd.

Answer:

length: \( 18 \) yd, width: \( 9 \) yd