Question

the length of a rectangle is six times its width. if the perimeter of the rectangle is 98 ft, find its area.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) ft. Then the length \( l = 6w \) ft.

Step2: Use perimeter formula

The perimeter of a rectangle is given by \( P = 2(l + w) \). We know \( P = 98 \) ft, so substitute \( l = 6w \) into the formula:
\( 98 = 2(6w + w) \)

Step3: Simplify and solve for \( w \)

Simplify the equation: \( 98 = 2(7w) = 14w \). Then solve for \( w \): \( w=\frac{98}{14}=7 \) ft.

Step4: Find length

Since \( l = 6w \), substitute \( w = 7 \): \( l = 6\times7 = 42 \) ft.

Step5: Calculate area

The area of a rectangle is \( A = l\times w \). Substitute \( l = 42 \) and \( w = 7 \): \( A = 42\times7 = 294 \) \( \text{ft}^2 \).

Answer:

294