SOLUTION: if a rectangle has a diagonal of 40 inches what is the height and width if the width is 8 inches longer than the height?

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Question 469112: if a rectangle has a diagonal of 40 inches what is the height and width if the width is 8 inches longer than the height?
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
Let x is the height of a rectangle
If the width is 8 inches longer than the height, then the width is %28x%2B8%29 inches
Use the Pythagorean theorem
x%5E2%2B%28x%2B8%29%5E2=40%5E2
x%5E2%2Bx%5E2%2B16x%2B64-1600=0
2x%5E2%2B16x-1536=0 divide by 2
x%5E2%2B8x-768=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-8+%2B-+sqrt%288%5E2-4%2A1%2A%28-768%29+%29%29%2F%282%2A1%29+
x+=+%28-8+%2B-+sqrt%283136%29%29%2F2+
x+=+%28-8+%2B56%29%2F2=24+ inches is the height of a rectangle
x+=+%28-8+-56%29%2F2=-32%3C0+ the extraneous root
The height of a rectangle is 24 inches, the width is 24+8=32 inches
Answer: 24 inches, 32 inches