Question

Tim wants to build a rectangular fence around his yard. He has 42
feet of fencing. If he wants the length to be twice the width, what is the largest possible length? Write an equation and solve.

A) 4w+4=42;l=18
B) 4w+8=42;l=16
C) 6w-42;l=7
D) 6w=42;l=14

Answer 1

Using the perimeter concept, it is found that:

D) 6w=42;l=14

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The perimeter of a rectangle of length l and width w is given by:

$P = 2(l + w)$

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42 feet of fencing means that $P = 42$

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Length twice the width, thus:

$l = 2w$

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Solving the equation:

$P = 2(l + w)$

$42 = 2(2w + w)$

$6w = 42$

$w = \frac{42}{7} = 7$

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The length is:

$l = 2w = 2(7) = 14$

Thus, the correct option is:

D) 6w=42;l=14

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