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.

$c = 3 b + 3$ $c = 3b+3$

$\frac{b . c}{2} = 84$ $(b.c)/2=84$

$\frac{b . (3 b + 3)}{2} = 84$ $(b.(3b+3))/2=84$

$3 b^{2} + 3 b = 84 \times 2$ $3b^2+3b=84xx2$

$3 b^{2} + 3 b - 168 = 0$ $3b^2+3b-168=0$

Solving the quadratic equation:

$b_{1} = 7$ $b_1=7$
$b_{2} = - 8$ $b_2=-8$ (impossible)

So, $b = 7$ $b=7$

$c = 3 \times 7 + 3 = 24$ $c=3xx7+3=24$

$a^{2} = 7^{2} + 24^{2}$ $a^2=7^2+24^2$

$a^{2} = 625$ $a^2=625$

$a = \sqrt{625} = 25$ $a=sqrt(625) = 25$

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