SOLUTION: a right angled triangle has a perimeter of 40 and an area of 60,what are the lengths of the sides

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Question 897380: a right angled triangle has a perimeter of 40 and an area of 60,what are the lengths of the sides
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the sides be x and y.
For area,
A=%281%2F2%29xy=60
xy=120
For perimeter,
P=x%2By%2Bsqrt%28x%5E2%2By%5E2%29
x%2By%2Bsqrt%28x%5E2%2By%5E2%29=40
From area,
y=120%2Fx
Substitute,
x%2By%2Bsqrt%28x%5E2%2By%5E2%29=40
x%2B120%2Fx%2Bsqrt%28x%5E2%2B14400%2Fx%5E2%29=40
x%2B120%2Fx%2Bsqrt%28x%5E4%2Fx%5E2%2B14400%2Fx%5E2%29=40
x%2B120%2Fx%2Bsqrt%28%28x%5E4%2B14400%29%2Fx%5E2%29=40
x%2B120%2Fx%2B%281%2Fx%29%2Asqrt%28x%5E4%2B14400%29=40
x%5E2%2B120%2Bsqrt%28x%5E4%2B14400%29=40x
sqrt%28x%5E4%2B14400%29=-x%5E2%2B40x-120
x%5E4%2B14400=x%5E4-80x%5E3%2B1840x%5E2-9600x%2B14400
-80x%5E2%2B1840x-9600=0
x%5E2-23x%2B120=0
%28x-8%29%28x-15%29=0
Two solutions:
x-8=0
x=8
Then,
y=120%2F8=15
and
x-15=0
x=15
Then,
y=120%2F15=8
The two sides are 8 and 15 and the hypotenuse is
8%2B15%2BH=40
H=17