Question

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

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ yards. Then the length $l = 6w$ yards.

Step2: Use perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Substitute $l = 6w$ and $P = 98$ into the formula:
$98=2(6w+w)$

Step3: Simplify the equation

First, simplify the right - hand side: $6w + w=7w$, so the equation becomes $98 = 2\times7w$, which is $98=14w$.

Step4: Solve for $w$

Divide both sides of the equation $98 = 14w$ by 14: $w=\frac{98}{14}=7$ yards.

Step5: Find the length

Since $l = 6w$, substitute $w = 7$ into it, then $l=6\times7 = 42$ yards.

Step6: Calculate the area

The area formula of a rectangle is $A=l\times w$. Substitute $l = 42$ and $w = 7$ into it: $A=42\times7 = 294$ square yards.

Answer:

$294$