The length of the longer leg of a right triangle is 22cm more than six times the length of the shorter leg.

Question

The length of the longer leg of a right triangle is
22cm
more than six times the length of the shorter leg. The length of the hypotenuse is
23cm
more than six times the length of the shorter leg. Find the side lengths of the triangle.

 

SHORTER =

LONGER=

HYPOTENUSE

Answer 1

Again, let's define some variables first.....

short leg = S

Long leg = 6S + 22

Hypotenuse = 6S + 23

now use our good friend Pythogoras, and don't get scared by the big numbers, just carry them along.

S² + (6S + 22)² = (6S + 23)²

 

S² + 36S² + 264S + 484 = 36S² +276S + 529 >>> lucky that the 36 S² cancels since it's on both sides of the equation.

 

so let's collect like terms on the left:

s² -12S - 45 = 0

 

now we gotta factor (s -15)(s+3) = 0

 

we can discard the s +3 factor because it results in a negative value for s when we use the zero product property to solve for s.

 

short side is 15

long side is 15*6 + 22 = 112

hypotenuse is 15*6 + 23 = 113