Question

1. if the perimeter of a rectangle is 76 cm, and the length is 8 cm longer than the width, what is the width?

Explanation:

Step1: Set up variables

Let the width of the rectangle be $x$ cm. Then the length is $(x + 8)$ cm.

Step2: Use the perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 76$ cm, we have $76=2((x + 8)+x)$.

Step3: Simplify the equation

First, simplify the right - hand side: $76=2(2x + 8)$. Then distribute the 2: $76 = 4x+16$.

Step4: Solve for $x$

Subtract 16 from both sides: $76-16=4x$, so $60 = 4x$. Divide both sides by 4: $x=\frac{60}{4}=15$.

Answer:

15 cm