SOLUTION: i have another ?
The longer leg of a right triangle has length 1cm less than twice the shorter leg. the hypotenuse has length 1cm greater than the shorter leg. find the lengths
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Question 119171This question is from textbook
: i have another ?
The longer leg of a right triangle has length 1cm less than twice the shorter leg. the hypotenuse has length 1cm greater than the shorter leg. find the lengths of the three sides of the triangle.
i have:
x
1-x
2x-1
This question is from textbook
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I presume x to be the short leg, so your 2x - 1 representation would be correct for the longer leg, but the hypotenuse is then x + 1 rather than 1 - x.
Using Pythagoras:
Expand the binomials, collect terms, and solve
So or . But we can exclude the root because that would mean that all three sides of the triangle were of length 0 -- a very uninteresting triangle indeed. So, the short leg is cm, the hypotenuse is cm and the long leg is cm.
Check:
=
=
, Check!
Hope that helps.
John
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The legs are
,
The hypotenuse is
By the pythagorean teorem:
One of the factors has to be zero. Either
or
If , then and then one of the legs would be zero length, so
cm shortest leg
cm other leg
cm hypotenuse
The sides are 3/2, 2, 5/2
check:
OK
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