SOLUTION: The hypotenuse of an isosceles right triangle is 3 cm longer than either of its legs. Find the exact length of each side

Algebra.Com
Question 436003: The hypotenuse of an isosceles right triangle is 3 cm longer than either of its legs. Find the exact length of each side
Answer by jorel1380(3719)   (Show Source): You can put this solution on YOUR website!
If it's an isosceles right triangle, then the legs are equal, therefore:
x2+x2=(x+3)2
2x2=x2+6x+9
x2-6x-9=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=72 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 7.24264068711928, -1.24264068711928. Here's your graph:

Throwing out the negative answer, the legs are 7.24264 cm., the hypotenuse is 10.24264 cm..
RELATED QUESTIONS

the hypotenuse of an isosceles right triangle is 10 centimeters longer than either of its (answered by Fombitz)
the hypotenuse of an isosceles right triangle is one meter longer than either of its... (answered by josmiceli)
The hypotenuse of an isosceles right triangle is 7 centimeters longer than either of its... (answered by mananth)
the hypotenuse of an isosceles right triangle is 7 centimeters longer than either of its... (answered by mananth,ewatrrr)
Hypotenuse of an isosceles right triangle is 9 feet longer than either of its legs. Find... (answered by edjones)
The hypotenuse of an isosceles right triangle is 2 centimeters longer than either of its... (answered by mananth)
The hypotenuse of an isosceles right triangle is 2 cm longer than either of its legs.... (answered by greenestamps)
An isosceles right triangle with legs of 3 units; find the length of the hypotenuse (answered by robertb)
The hypotenuse of an isosceles right triangle measures 16 cm. Find the length of a... (answered by ewatrrr)