Question

the length of a rectangle is four times its width. if the perimeter of the rectangle is 100 in, find its length and width.

Explanation:

Step1: Set up variables

Let the width of the rectangle be \( w \) inches. Then the length \( l = 4w \) inches.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P=2(l + w) \). Substitute \( l = 4w \) and \( P = 100 \) into the formula:

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Step3: Solve for \( w \)

Divide both sides of the equation \( 100 = 10w \) by \( 10 \):

$$w=\frac{100}{10}=10$$

Step4: Solve for \( l \)

Since \( l = 4w \), substitute \( w = 10 \):

$$l=4\times10 = 40$$

Answer:

length: \( 40 \) in, width: \( 10 \) in