# RT 10

Area of right triangle is 84 cm2 and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.

Result

x =  46.35 cm

#### Solution:

$x = a+b+c \ \\ \ \\ a = 10 \ cm \ \\ S = 84 \ cm^2 \ \\ S = ab/2 \ \\ \ \\ b = 2S/a= 2\cdot 84 / 10 = 16.8 \ cm \ \\ \ \\ c^2 = a^2 + b^2 \ \\ c = \sqrt{ a^2 + b^2 } = \sqrt{ 10^2 + 16.8^2} = 19.55\ cm \ \\ \ \\ x = a+b+c = 46.35 \ \text{cm}$

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