Question 837707
The area of a right angled-triangle is 180 sq m and its perimeter is 90 m. Find the hypotenuse.
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Area = a*b/2 = 180
b = 360/a
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{{{c = sqrt(a^2 + b^2) = 90 - a - b}}}
{{{sqrt(a^2 + (360/a)^2) = 90 - a - 360/a}}}
{{{a*sqrt(a^2 + (360/a)^2) = 90a - a^2 - 360}}}
{{{sqrt(a^4 + 129600) = 90a - a^2 - 360}}}
{{{a^4 + 129600 = a^4 - 180a^3 + 8820a^2 - 64800a + 129600}}}
{{{0 = - 180a^3 + 8820a^2 - 64800a}}}
{{{180a^2 - 8820a + 64800 = 0}}}
{{{a^2 - 49a + 360 = 0}}}
a = 9, a = 40
--> c = 41 meters