SOLUTION: Hello, I don't understand how to figure out this word problem that I have to solve using the Pythagorean theorem. "The diagonal of a rectangle is 3 ft longer than its length and 5

Algebra ->  Pythagorean-theorem -> SOLUTION: Hello, I don't understand how to figure out this word problem that I have to solve using the Pythagorean theorem. "The diagonal of a rectangle is 3 ft longer than its length and 5      Log On


   

Question 1022854: Hello, I don't understand how to figure out this word problem that I have to solve using the Pythagorean theorem. "The diagonal of a rectangle is 3 ft longer than its length and 5 ft longer than its width. What is the area of the rectangle?" I appreciate any help!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Dimension sizes of the rectangle: w and L
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system%28h=3%2BL%2Ch=5%2Bw%29


Let h be hypotenuse same as a diagonal.
w%5E2%2BL%5E2=h%5E2


Substitute for L and for w in the Pythagorean Theorem formula equation.
system%28L=h-3%2Cw=h-5%29
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%28h-5%29%5E2%2B%28h-3%29%5E2=h%5E2
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Solve for h, first.
h%5E2-10h%2B25%2Bh%5E2-6h%2B9=h%5E2
h%5E2-10h-6h%2B34=0
h%5E2-16h%2B34=0
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General Formula Solution for Quadratic Equation:
h=%2816%2B-+sqrt%2816%5E2-4%2A34%29%29%2F2
h=%2816%2B-+sqrt%284%2A4%2A4%5E2-4%2A34%29%29%2F2
h=%2816%2B-+2%2Asqrt%2848-34%29%29%2F2
h=8%2B-+sqrt%2814%29, take the PLUS form.
highlight%28h=8%2Bsqrt%2814%29%29


Evaluating the dimension measurements:
L=h-3
L=5%2Bsqrt%2814%29
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w=h-5
w=3%2Bsqrt%2814%29
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AREA of the rectange,
wL=%285%2Bsqrt%2814%29%29%283%2Bsqrt%2814%29%29
15%2B8sqrt%2814%29%2B14
highlight%2829%2B8sqrt%2814%29%29