Question

1. the perimeter of a rectangle is 24 inches. the length is three times the width. find the dimensions.

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ inches. Then the length $l = 3w$ inches.

Step2: Use the perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 24$ inches. Substitute $l = 3w$ into the formula: $24=2(3w+w)$.

Step3: Simplify the equation

First, simplify the right - hand side: $2(3w + w)=2(4w)=8w$. So the equation becomes $8w = 24$.

Step4: Solve for $w$

Divide both sides of the equation $8w = 24$ by 8: $w=\frac{24}{8}=3$ inches.

Step5: Solve for $l$

Since $l = 3w$, substitute $w = 3$ into the equation: $l=3\times3 = 9$ inches.

Answer:

The width is 3 inches and the length is 9 inches.