SOLUTION: The shortest leg of a triangle is 7 inches shorter than the other leg. The hypotenuse of this triangle is 13 inches. What are the lengths of the two legs of this triangle?

Algebra.Com
Question 1164390: The shortest leg of a triangle is 7 inches shorter than the other leg. The hypotenuse of this triangle is 13 inches. What are the lengths of the two legs of this triangle?
Answer by ikleyn(52814)   (Show Source): You can put this solution on YOUR website!
.

The second famous Pythagorean triple after (3,4,5)  with  3^2 + 4^2 = 5^2


is (5,12,13)  with  5^2 + 12^2 = 25 + 144 = 169 = 13^2.


So, your triangle is (5,12,13) inches.    ANSWER



Alternatively,  you can solve this quadratic equation

    x^2 + (x-7)^2 = 13.


You will get the same triangle, then.


After doing some work, of course.

Solved.



RELATED QUESTIONS

The shortest leg of a triangle is 7 inches shorter than the other leg. The hypotenuse of... (answered by Tatiana_Stebko)
The shortest leg of a triangle is 17 inches shorter than the other leg. The hypotenuse of (answered by Fombitz)
The shortest leg of a triangle is 7 centimeters shorter than the other leg. The... (answered by Edwin McCravy)
One leg of right triangle is 9 inches shorter than the other leg. The hypotenuse is 45... (answered by nerdybill)
The shortest leg of a triangle is 7 feet shorter than the other leg. The hypotenuse of... (answered by josgarithmetic)
One leg of a right triangle is once inch shorter than the other leg.If the hypotenuse is... (answered by MathLover1,MathTherapy)
One leg of a right triangle is 4 inches longer than the other. The hypotenuse of the... (answered by ankor@dixie-net.com)
In a right triangle, the length of the longer leg is 7 more inches than the shorter leg.... (answered by Cromlix)
In a right triangle, the longer leg is 7 inches more than the shorter leg, and the... (answered by josgarithmetic)