Geo-easy
Geometry
Level
3
The perimeter of a right triangle is 180 units while its area is 360 square units. What is the length of its hypotenuse?
The answer is 86.
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1 solution
a^2+b^2=c^2
a+b+c=180
(1/2)ab=360; 2ab=1440
a^2+b^2+2ab=1440+c^2
(a+b)^2=1440+c^2
(180-c)^2=1440+c^2
32400-360c+c^2=1440+c^2
360c=30960
c=86