RT leg and perimeter

Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.

Result

a =  84
b =  73.43
c =  111.57

Solution:

a=84 o=269a=84 \ \\ o = 269
a2+b2=c2 a+b+c=o  7056=c2−b2 b+c=185  7056=c2−(185−c)2 7056=c2−(1852−2⋅185⋅c+c2) 7056=−1852+370c 41281=370c c=111.57 b=185−c=73.43 a^2+b^2=c^2 \ \\ a+b+c=o \ \\ \ \\ 7056 = c^2-b^2 \ \\ b+c=185 \ \\ \ \\ 7056 = c^2-(185-c)^2 \ \\ 7056 = c^2-(185^2-2\cdot 185\cdot c+c^2) \ \\ 7056 = -185^2+370 c \ \\ 41281 = 370 c \ \\ c = 111.57 \ \\ b= 185-c = 73.43 \ \\

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