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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Question 198554This question is from textbook
: 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
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)
