SOLUTION: a rectangle has perimeter 62 and area 136. what is the length of the rectangle's diagonal?

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Question 888596: a rectangle has perimeter 62 and area 136. what is the length of the rectangle's diagonal?
Answer by lwsshak3(11628) About Me  (Show Source):
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a rectangle has perimeter 62 and area 136. what is the length of the rectangle's diagonal?
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let x=length of rectangle
let y=width of rectangle
2x+2y=perimeter=62
2y=62-2x
y=(62-2x)/2=31-x
length*width=area
x*y=136
x(31-x)=136
31x-x^2=136
x^2-31x+136
solve by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=1, b=-31, c=36
ans:
x=1.14 (reject)
or
x=29.36
y=62-2x=3.28
By the pythagorean theorem:
√(x^2+y^2)=diagonal
√(29.36^2+3.28^2)=√872.77
diagonal=29.54