SOLUTION: The sum of the legs of a right triangle is 17 in. The longer leg is 2 more than twice the shorter. Th hypotenuse is 13 in. Find the length of each leg. Isn't the formula for a righ

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Question 144667This question is from textbook Prealgebra & Introductory Algebra
: The sum of the legs of a right triangle is 17 in. The longer leg is 2 more than twice the shorter. Th hypotenuse is 13 in. Find the length of each leg. Isn't the formula for a right triangle a^2 +b^2=c^2? From what I understand this is the way I would write to solve, but it doesn't make sense to me.
17=a^2+b^2+2
a^2+b^2= 13^2
Thanks for your help. This question is from textbook Prealgebra & Introductory Algebra

Found 3 solutions by solver91311, scott8148, ankor@dixie-net.com:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Length of one leg: a

Length of the other leg: b

Assume b is the long leg, so b+=+2a+%2B+2 (2 more than twice the shorter)

Sum of the lengths of the legs: a+%2B+b+=+17, but since b=2a%2B2, a%2B2a%2B2=17 by substitution.

Collect like terms and solve for a, 3a%2B2=17 => 3a=15 => a=5

So: 5+%2B+b+=+17 => b=12

Check:
5%5E2%2B12%5E2=25%2B144=169=13%5E2 Checks.

Note that if we had assumed in the beginning that a was the longer leg, the result would have been that a=12 and b=5 -- same answer for all practical purposes.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x="shorter leg"

"The longer leg is 2 more than twice the shorter" __ 2x+2

"The sum of the legs of a right triangle is 17 in." __ x+2x+2=17

3x+2=17 __ 3x=15 __ x=5

substituting __ 2(5)+2=12

5,12,13 is a Pythagorean triple (like 3,4,5) __ 5^2+12^2=13^2 __ 25+144=169

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the legs of a right triangle is 17 in. The longer leg is 2 more than twice the shorter. The hypotenuse is 13 in. Find the length of each leg.
:
Isn't the formula for a right triangle a^2 +b^2 = c^2? Yes it is, but we don't need it here.
:
It says,"The hypotenuse is 13 in." therefore
c = 13
:
Let a = shorter leg
:
then it says,"The longer leg is 2 more than twice the shorter."therefore
b = 2a+2
:
"the sum of the legs of a right triangle is 17":
a + b = 17
:
Substitute (2a+2) for b and 13 for c, find a:
a + (2a+2) = 17
:
3a + 2 = 17
:
3a = 17 - 2
:
3a = 15
a = 15%2F3
a = 5
:
Find the longer leg (b):
b = 2(5) + 2
b = 12
:
We can confirm our solution using the pythag
Does 5^2 + 12^2 = 13^2?