Pythagorean Theorem

Question

The shorter leg of a right triangle is 9 cm shorter than the longer leg. The hypotenuse is 9 cm longer than the longer leg. Find the side lengths of the triangle. 

Answer 1

Let x = the long leg, then x-9 is the short leg and the hypotenuse is x+9, 

 

x² + (x-9)² = (x+9)²

 

X² + x² -18x +81 = x² +18x + 81

 

x² - 36x = 0

 

(x-36)x = 0

 

X is either 0 (which is impossible) or 36

Answer 2

What fun!!

 

Let's let l = the longer leg.

 

That makes the shorter leg l-9 and the hypotenuse l+9. The Pythagorean Theorem gives us:

 

(l-9) ² + l² = (l + 9)²

 

l² - 18l + 81 +l² = l² +18l +81 Subtract the right side from both sides and you get:

 

l² -36l = 0 factor out an l:

 

l(l-36) = 0 This means that l either equals zero (this obviously can't be true) or l=36.

 

So the 3 sides should be 27 , 36 and 45. (if you know about a 3,4,5 triangle you will see it's a great answer)