SOLUTION: The hypotenuse of a right triangle is three less than twice the shorter leg. The length of the other leg is three more than the shorter leg find the length of the shorter leg

Algebra ->  Pythagorean-theorem -> SOLUTION: The hypotenuse of a right triangle is three less than twice the shorter leg. The length of the other leg is three more than the shorter leg find the length of the shorter leg      Log On


   

Question 1177212: The hypotenuse of a right triangle is three less than twice the shorter leg. The length of the other leg is three more than the shorter leg find the length of the shorter leg
Answer by MathLover1(20849) About Me  (Show Source):
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let’s hypotenuse be c, the shorter leg b, and the other leg a
given:
The hypotenuse of a right triangle is three less than twice the shorter leg.
c=2b-3
The length of the other leg is three more than the shorter leg.
a=b%2B3
use Pythagorean theorem:
c%5E2=a%5E2%2Bb%5E2.............substitute c and a
%282b-3%29%5E2=%28b%2B3%29%5E2%2Bb%5E2.......solve for b
4b%5E2-12b%2B9=b%5E2%2B6b%2B9%2Bb%5E2
4b%5E2-12b%2B9=2b%5E2%2B6b%2B9
4b%5E2-12b%2B9-2b%5E2-6b-9=0
2b%5E2-18b=0
2b%28b-9%29=0
=> highlight%28b=9%29=> the length of the shorter leg

go to
a=b%2B3.......substitute b
a=9%2B3
a=12
c=2b-3
c=2%2A9-3
c=15