Question

the length of a rectangle is 5 yd longer than its width. if the perimeter of the rectangle is 54 yd, find its length and width. length: yd width: yd

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ yd. Then the length $l = w + 5$ yd.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 54$ yd, we substitute $l$ and $P$ into the formula: $54=2((w + 5)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $54=2(2w + 5)$. Then distribute the 2: $54 = 4w+10$.

Step4: Solve for $w$

Subtract 10 from both sides: $54−10=4w$, so $44 = 4w$. Divide both sides by 4: $w=\frac{44}{4}=11$ yd.

Step5: Solve for $l$

Since $l=w + 5$, substitute $w = 11$ into the equation: $l=11 + 5=16$ yd.

Answer:

length: 16 yd
width: 11 yd