Problema Solution

Please help me to solve this :

The hypotenuse of a right triangle is 6 more than the shorter leg. The longer leg is three more than the shorter leg. Find the length of the shorter leg

Hint: Draw a right triangle and apply the Pythagorean Theorem

Answer provided by our tutors

Short leg is a=x

Hypothenuse is h=x+6

Long leg is b=x+3

h^2 =  a^2 + b^2

(x+6)^2 = x^2 + (x+3)^2

x2 + 12x + 36 = x2 + x2 + 6x + 9 

Rearrange

-x2 + 6x +27 = 0

Factor

(-x+9)(x+3)=0

x is either 9 or -3. -x is an impossible value, so the short leg has length 9.