SOLUTION: The perimeter of a rectangle is 32ft. Find the dimensions if the length is 4ft longer than 3 times the width.

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Question 119609This question is from textbook
: The perimeter of a rectangle is 32ft. Find the dimensions if the length is 4ft longer than 3 times the width. This question is from textbook

Answer by Caallen2(9) (Show Source):
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First, perimeter (P) is 2 times length plus 2 times width. P = 2L + 2W.
Since the length is 4 more than 3 times the width let width = x and length = 3x + 4. Plug this into an equation.
P = 32
W = x
L = 3x + 4
2(3x +4)+ 2(x) = 32
Use the distributive property.
6x + 8 + 2x = 32
Combine like terms.
8x + 8 = 32
Subtract 8 from both sides.
8x = 24.
Solve for x by dividing both sides by 8.
x = 3.
Now substitute 3 in the formula for length.
L = 3x + 4
= 3(3) + 4
= 9 + 4
= 13
Therefore width = 3 and length = 13.