The Diagonal Of A Rectangle Is Twenty-five Inches More Than Its Width. The Length Of The Rectangle Is 17 Inches More That Its Width. What Are The Dimensions Of The Rectangle?
Answer:
Let the diagonal be represented by d, and let the length and width be represented by l and w, respectively.
d = w+25 (the diagonal is 25 more than the width)
l = w+17 (the length is 17 more than the width)
d2 = w2 + l2 (the Pythagorean Theorem)
Substituting the first two equations into the last, we acquire
(w+25)2 = w2 + (w+17)2
w2 + 50w + 625 = w2 + w2 + 34w + 289 (expanding the squared expressions)
0 = w2 - 16w - 336 (subtract the left side from both sides)
w = (-(-16) ±√((-16)2-4(1)(-336)))/(2*1) (use the quadratic formula to find w)
w = (16 ±√(256+1344))/2 (evaluate)
w = (16 ±√1600)/2
w = (16±40)/2
w = 8±20 = {28, -12}
l = 28+17 = 42
d = 28+25 = 53
Only the positive solution will work for a measured value.
width = 28 inches
length = 42 inches
diagonal = 53 inches
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