The legs of a right triangle have lengths of x + 4 and x + 7. The hypotenuse length is 3x. How do you find the perimeter of the triangle?
1 Answer
Jan 3, 2016
Explanation:
The perimeter is equal to the sum of the sides, so the perimeter is:
#(x+4)+(x+7)+3x=5x+11#
However, we can use the Pythagorean theorem to determine the value of
#a^2+b^2+c^2#
where
Plug in the known side values.
#(x+4)^2+(x+7)^2=(3x)^2#
Distribute and solve.
#x^2+8x+16+x^2+14x+49=9x^2#
#2x^2+22x+65=9x^2#
#0=7x^2-22x-65#
Factor the quadratic (or use the quadratic formula).
#0=7x^2-35x+13x-65#
#0=7x(x-5)+13(x-5)#
#0=(7x+13)(x-5)#
#x=-13/7,5#
Only
Since
#5(5)+11=36#