# Chapter 2 - Section 2.5 - An Introduction to Problem Solving - Exercise Set - Page 166: 34

The length of the rectangular field is $120$ yards and the width is $24$ yards.

#### Work Step by Step

We know that the formula for the perimeter of a rectangle is: $$P = 2l + 2w$$ We know from the problem that the perimeter is $288$ yards and the length is five times the width, $w$, so we can express the length in terms of width as follows: $$l = 5w$$ We can now put together the equation using what we know from the problem: $$288 = 2(5w) + 2w$$ We can now simplify the equation: $$10w + 2w = 288$$ Combine like terms: $$12w = 288$$ Solve for $w$ by dividing both sides by $12$: $$w = 24$$ We now plug $24$ back into the equation to find $l$. If $l = 5w$, then: $$l = 5(24)$$ $$l = 120$$ The length of the rectangular field is $120$ yards and the width is $24$ yards.

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