Question

a rectangular athletic field is twice as long as it is wide. if the perimeter of the athletic field is 120 yards, what are its dimensions? the width is 20 yards. the length is yards.

Explanation:

Step1: Define variables

Let the width of the field be $w$ yards. Then the length $l = 2w$ yards.

Step2: Use perimeter formula

The perimeter formula for a rectangle is $P=2(l + w)$. Given $P = 120$ yards, substitute $l = 2w$ into the formula: $120=2(2w+w)$.

Step3: Simplify the equation

First, simplify the right - hand side: $2(2w + w)=2(3w)=6w$. So, the equation becomes $6w = 120$.

Step4: Solve for $w$

Divide both sides of the equation $6w = 120$ by 6: $w=\frac{120}{6}=20$ yards.

Step5: Find the length

Since $l = 2w$ and $w = 20$ yards, then $l=2\times20 = 40$ yards.

Answer:

40