SOLUTION: One side of a rectangle is 9 ft. longer than the adjacent side. the length of the diagonal is 45 ft. find the dimensions of the rectangle

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Question 195188This question is from textbook amsco's geometry
: One side of a rectangle is 9 ft. longer than the adjacent side. the length of the diagonal is 45 ft. find the dimensions of the rectangleThis question is from textbook amsco's geometry

Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!


As per given condition, one side of a rectangle is 9ft longer than the adjacent side.
If adjacent side equals x (ft), then
this shows the length of the opposite side = x + 9 (ft).

With the diagonal side given which serves as the hypotenuse = 45 (ft) that forms a Right triangle.
drawing%28300%2C300%2C-1%2C5%2C-1%2C7%2Cline%280%2C0%2C0%2C6%29%2Cline%280%2C6%2C3%2C6%29%2Cgreen%28line%283%2C6%2C3%2C0%29%29%2Cgreen%28line%283%2C0%2C0%2C0%29%29%2Cgreen%28line%280%2C0%2C3%2C6%29%29%2Cgreen%28locate%283.2%2C3%2Cx%2B9%29%29%2Cgreen%28locate%281.5%2C-.2%2Cx%29%29%2Cgreen%28locate%281.5%2C4.5%2C45ft%29%29%2Clocate%281.5%2C-.6%2Cadj%29%2Clocate%283.2%2C3.8%2Copp%29%2Clocate%281.1%2C4%2Chyp%29%29
By Pyth.Theorem:
adj%5E2%2Bopp%5E2=hyp%5E2
x%5E2%2B%28x%2B9%29%5E2=45%5E2
x%5E2%2Bx%5E2%2B18x%2B81=2025
2x%5E2%2B18x%2B81-2025=0
2x%5E2%2B18x-1944=0

*Notesystem%28a=2%2Cb=18%2Cc=%28-1944%29%29

Solving discriminant: b%5E2-4ac=18%5E2-4%282%29%28-1944%29=324%2B15552=red%2815876%29

Then,
x=%28-18%2B-sqrt%2815876%29%29%2F%282%2A2%29=%28-18%2B-126%29%2F4
x=%28-18%2B126%29%2F4=108%2F4=red%2827ft%29 ---> adjacent = Width
x=%28-18-126%29%2F4=-144%2F4=-36, disregard "-"

Then,9ft%2Bx=9ft%2B27=red%2836ft%29 ---> opposite side = Length.

Check, Pyth.Theorem:
adj%5E2%2Bopp%5E2=hyp%5E2
27%5E2%2B36%5E2=45%5E2
729%2B1296=2025ft%5E2
2025ft%5E2=2025ft%5E2

Thank you,
Jojo