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A rectangle's perimeter is 80 ft. Its length is 4 ft shorter than three times its width. Use an equation to find the rectangle's length and width

User Steve Moseley
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1 Answer

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25 votes

Question:

A rectangle's perimeter is 80 ft. Its length is 4 ft shorter than three times its width. Use an equation to find the rectangle's length and width​.

Solution:

Let's denote by L the length of the rectangle, and by W its width. Now, if the length is 4 ft shorter than three times its width, we have the following diagram:

Then, we have the following equation:


2(3W-4)\text{ + 2W = 80 = perimeter}

this is equivalent to:


6W\text{ -8 + 2W = 80}

this is equivalent to:


8W\text{ = 80 +8 = 88}

solving for W, we obtain:


W\text{ = }(88)/(8)=\text{ 11}

then, the width is 11 and the length would be:


L\text{ = 3W -4 = 3(11) -4 = 29}

then, we can conclude that the correct answer is:

Length = 29

Width = 11

A rectangle's perimeter is 80 ft. Its length is 4 ft shorter than three times its-example-1
User Orcris
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