The Diagonal Of A Rectangle Is 25 Inches More Than Its Width. The Length Of The Rectangle Is 17 Inches More Than Its Width. What Are The Dimensions Of The Rectangle?
Answer:
Let w represent the width of the rectangle. The problem statement, together with the Pythagorean Theorem, tells us
w2 + (w+17)2 = (w+25)2
w2 + w2 + 34w + 289 = w2 + 50w + 625 (multiply everything out)
w2 - 16w - 336 = 0 (subtract the right side from both sides)
This can probably be solved by factoring. To do so, we entail to find factors of 336 that differ by 16.
336 = 24*3*7 = 8*42 = 12*28 = 14*24
This suggests the factorization
(w-28)(w+12) = 0
Solutions to this are w=28, w=-12. Only the positive solution is of interest.
The rectangle is 28 inches wide and 45 inches long. It has a diagonal of 53 inches.
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