The longer leg of a right triangle is 3 inches more than 3 times the length of the shorter leg. The area of the triangle is 84 square inches. How do you find the perimeter of a right triangle?

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Answer 1 · 2015-10-19T00:10:00

P = 56 square inches.

See figure below for better understanding.

#c = 3b+3#

#(b.c)/2=84#

#(b.(3b+3))/2=84#

#3b^2+3b=84xx2#

#3b^2+3b-168=0#

Solving the quadratic equation:

#b_1=7#
#b_2=-8# (impossible)

So, #b=7#

#c=3xx7+3=24#

#a^2=7^2+24^2#

#a^2=625#

#a=sqrt(625) = 25#

#P=7+24+25=56# square inches