Two legs of a right triangle are 2 inches and 3 inches long. What is the length of the shorter leg of a similar right triangle if its longer leg is 12 inches long?

Step-by-step explanation:

a2+b2=c2

x2 + (x-2) 2=102

x2+x2-4x+4=100

2x2-4x+4-100=0

2x2-4x-96=0

divide both sides by 2

x2-2x-48=0

factor

(x-8) (x+6) = 0

x-8=0

x=8 inches

x-2=6 inches

x and x-2 are the legs and the hypotenuse is 10 inches