1) Let's starting by defining the terms.
Shorter leg= S
Longer leg= L
Hypotenuse= H
2) This question has three unknown variables, so we need a system three equations to solve them.
3)The question gives us two equations:
L=S+88 (Long leg is 88 feet more than short leg)
H=2S-88 (Hypotenuse is twice the short leg in length, minus 88 feet)
4) We know from Pythagorean theorem that the two sides of a right triangle have a relationship to the hypotenuse described by:
A2 + B2 = C2
5) Using our definitions in step 1, we can rewrite this as:
S2 + L2 = H2
6) Now we have three equations and three unknowns:
A) L=S+88
B) H=2S-88
B) H=2S-88
C) S2 + L2 = H2
7) By substituting equation A into equation C, we get one equation with two unknowns:
S2 + (S+88)2 = H2
7a) By substituting equation B into this equation, we get one equation with one unknown:
S2 + (S+88)2 = (2S-88)2
S2 + S2 + (2*88S) + 882 = 4S2 - (4*88S) - 882
We start to simplify: 882 cancels out
2S2 + (2*88S) = 4S2 - (4*88S)
We continue to simplify: Divide by two, and get all terms on same side of equation
S2 +88S = 2S2 -(2*88S)
0 = S2 - (2*88S) - (88S)
0 = S2 - (3*88S)
0 = S - (3*88)
S = 3*88 = 264
S = 3*88 = 264
The short side of the triangle is 264 feet.
8) VERY IMPORTANT! We must check this with the other equations:
A) L=S+88 = 264 +88
L= 352
B) H=2S-88 = (2*264) - 88
H =440
C) S2 + L2 = H2
2642 + 3522 = 4402 ?
69696 + 123904 =193600 ?
Yes, it does, the answer is correct.
Rob R.
05/18/16