SOLUTION: One leg of a right triangle is once inch shorter than the other leg.If the hypotenuse is 5 inches , find the length of the shorter leg.

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Question 1125269: One leg of a right triangle is once inch shorter than the other leg.If the hypotenuse is 5 inches , find the length of the shorter leg.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let legs be a and b, and hypotenuse c

One leg of a right triangle is one inch shorter than the other leg, we have
a=b-1....eq.1


if the hypotenuse is 5 inches , find the length of the shorter leg using Pythagorean theorem
c%5E2=a%5E2%2Bb%5E2...eq.2
plug in a from eq.1 in eq.2 and c=5

5%5E2=%28b-1%29%5E2%2Bb%5E2...solve for b
25=b%5E2-2b%2B1%2Bb%5E2
25=2b%5E2-2b%2B1
25-1%5E2=2b%5E2-2b
0=2b%5E2-2b-24.............simplify
0=b%5E2-b-12
use quadratic formula:

b+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A%28-12%29+%29%29%2F%282%2A1%29+
b+=+%281+%2B-+sqrt%28+1%2B48+%29%29%2F2+
b+=+%281+%2B-+sqrt%28+49+%29%29%2F2+
b+=+%281+%2B-+7%29%2F2+
solution: we need only positive solution
b+=+%281+%2B+7%29%2F2+
b+=+8%2F2+
b+=+4+ inches
go to a=b-1....eq.1, substitute b
a=4-1
highlight%28a=3%29 inches ->the length of the shorter leg




Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

One leg of a right triangle is once inch shorter than the other leg.If the hypotenuse is 5 inches , find the length of the shorter leg.
SIMPLE 3-4-5 Pythagorean TRIPLE. 

3 (shorter leg); 4 (longer leg) ; 5 (Hypotenuse)