Question

the length of a rectangle is 2 cm longer than its width. if the perimeter of the rectangle is 48 cm, find its length and width. length: cm width: cm

Explanation:

Step1: Define variables

Let the width of the rectangle be $x$ cm. Then the length is $(x + 2)$ cm.

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2(l + w)$. Given $P = 48$ cm, we substitute $l=x + 2$ and $w=x$ into the formula: $48=2((x + 2)+x)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $48=2(2x + 2)$. Then distribute the 2: $48 = 4x+4$.

Step4: Solve for x

Subtract 4 from both sides: $48-4=4x$, so $44 = 4x$. Divide both sides by 4: $x=\frac{44}{4}=11$.

Step5: Find length and width

The width $x = 11$ cm. The length is $x + 2=11 + 2=13$ cm.

Answer:

length: 13 cm
width: 11 cm