# If c is the measure of the hypotenuse of a right triangle, how do you find each missing measure given a=x, b=x+7, c=97?

##### 1 Answer

Feb 26, 2017

#### Explanation:

By pythagorean theorem, we have

#a^2 + b^2 = c^2#

#x^2 + (x + 7)^2= 97^2#

#x^2 + x^2 + 14x + 49 = 9409#

#2x^2 + 14x - 9360 =0#

#x^2 + 7x - 4680 = 0#

#x = (-7 +- sqrt(7^2 - 4 * 1 * -4680))/(2 * 1)#

#x = (-7 +- 137)/2#

#x = -72 and 65#

Obviously, a triangle with negative lengths is impossible. Therefore, we have that

Hopefully this helps!