SOLUTION: If the length of a rectangle is 3 feet longer than the width and the diagonal is 15 feet, then what are the length and the width?
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: If the length of a rectangle is 3 feet longer than the width and the diagonal is 15 feet, then what are the length and the width?
This question is from textbook
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
If the length of a rectangle is 3 feet longer than the width and the diagonal is 15 feet, then what are the length and the width?
.
Let w = width of rectangle
then
w+3 = length
.
Applying Pythagorean theorem:
w^2 + (w+3)^2 = 15^2
w^2 + (w+3)(w+3) = 15^2
w^2 + (w^2+3w+3w+9) = 225
w^2 + w^2+6w+9 = 225
2w^2+6w+9 = 225
2w^2+6w-216 = 0
w^2+3w-108 = 0
Factoring:
(w-9)(w+12) = 0
w = {9, -12}
We can throw out the negative solution leaving us with:
w = 9 feet (width)
.
Length:
w+3 = 9+3 = 12 feet (length)
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