math question that i dont understand

Question

The length of the longer leg of a right triangle is 5 feet less than 3 times the length of the shorter leg.  The length of the hypotenuse is 13 feet less than 6 times the length of the shorter leg.  Find the sides of the triangle. 

Answer 1

The pythagorean theorum tells us that A² + B² = C²

Let's call the shorter leg A

The longer leg would be B=3A-5 (read it backwards - 5 less than 3 times A)

The hypoteneuse, C=6A-13. (Backwards it reads 13 less than 6 times A)

The pythagorean becomes:

A² + (3A-5)² = (6A-13)²

Expanding by the foil method:

A² + (9A² - 30A + 25) = (36A² -78A -78A + 169)

Combining like terms:

10A² - 30A +25 = 36A² -156A + 169

26A² -126A +145 = 0

Using the quadratic equation where A=26 B=-126 C= 144

The equation provides 2 answers, 3 and 1.84615, which yields a negative length hypoteneuse, which can be ignored.

For A=3, B=4 and C=5, which is the simplest whole number right triangle.