Question

the length of a rectangle is twice its width. if the perimeter of the rectangle is 48 in, find its length and width. length: in width: in

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ inches. Then the length $l = 2w$ inches.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $l = 2w$ and $P = 48$ into the formula: $48=2(2w+w)$.

Step3: Simplify the equation

First, simplify the right - hand side: $2(2w + w)=2(3w)=6w$. So the equation becomes $6w = 48$.

Step4: Solve for $w$

Divide both sides of the equation $6w = 48$ by 6: $w=\frac{48}{6}=8$ inches.

Step5: Solve for $l$

Since $l = 2w$, substitute $w = 8$ into the equation: $l=2\times8 = 16$ inches.

Answer:

length: 16 in
width: 8 in