SOLUTION: The diagonal of a rectangle is 10cm and the area of the rectangle is 22 cm^2. Find the perimeter of the rectangle

Question 495945: The diagonal of a rectangle is 10cm and the area of the rectangle is 22 cm^2. Find the perimeter of the rectangle
Answer by cleomenius(959) (Show Source): You can put this solution on YOUR website!
We will use two formulas.
First the formula for the area of a triangle, to obtain a value for y.
1/2*xy = 11 so y = 22/x
Now we substitute into y for the Pythagorean theory.
x^2 + y^2 = 10^2
x^2 + (22/x)^2 = 100
This equates to
x^4 -100x^2 + 484= 0
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Now we the Quadratic formula:
a = 1
b= -100
c = 484
We obtain:
x^2 = 94.9, 4.93
x = 9.74, 2.25
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To check:
9.74 * 2.25 = 21.915, approx 22.
Also
(9.74)^2 = 94.87
(2.25)^2 = 5.07
94.87 + 5.07 = 99.94 = diameter^2 = approx 10.
This does check.
Cleomenius.
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