The fence around Stan's rectangular backyard is 48 feet. His yard is 3 feet longer than twice its width. What is the length of Stan's yard?

Length = 17 ft

Concept:

Here, we need to know how to find the perimeter of a rectangle.

Perimeter (rectangle) = 2 (l + w)

l = length

w = width

If you are still confused, you may refer to the attachment below for a graphical explanation or tell me.

Solve:

**Disclaimer** I assume that the length is [3 feet longer than twice its width] because a [yard] would not use length to measure it. If it was, then you may refer to my answer. If it was not, then you may tell me and I will redo it.

Let x be the width

Let 2x + 3 be the length

Given information

Perimeter = 48 ft

width = x

length = 2x + 3

Given expression deducted from the question

Perimeter = 2 (l + w)

Substitute values into the expression

48 = 2 (2x + 3 + x)

Combine like terms in the parentheses

48 = 2 (2x + x + 3)

48 = 2 (3x + 3)

Expand parentheses and apply the distributive property

48 = 2 · 3x + 2 · 3

48 = 6x + 6

Subtract 6 on both sides

48 - 6 = 6x + 6 - 6

42 = 6x

Divide 6 on both sides

42 / 6 = 6x / 6

x = 7

Find the value of length

Length = 2x + 3 = 2(7) + 3 = 14 + 3 =

Hope this helps!! :)

Please let me know if you have any questions

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step-by-step explanation: