SOLUTION: What is the lenghts of the legs? The hypotenuse of a right triangle is 4 cm long. One leg is 1 cm longer than the other. Find the lengths of the legs. Round to the nearest tenth

Question 565570: What is the lenghts of the legs?
The hypotenuse of a right triangle is 4 cm long. One leg is 1 cm longer than the other. Find the lengths of the legs. Round to the nearest tenth.
Thank You =)

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The hypotenuse of a right triangle is 4 cm long.
One leg is 1 cm longer than the other. Find the lengths of the legs.
Round to the nearest tenth.
:
Let x = one leg
then
(x+1) = the other leg
:
Remember our good friend pythag, a^2 + b^2 = c^2, so we have
x^2 + (x+1)^2 = 4^2
FOIL (x+1)(x+1)
x^2 + x^2 + 2x + 1 = 16
combine like terms on the left to reveal our old friend, the quadratic equation!
2x^2 + 2x + 1 - 16 = 0
2x^2 + 2x - 15 = 0
Unfortunately this will not factor, use the quadratic formula:

In this equation: a=2, b=2, c=-15

the positive solution is all we want here

x =
x = 2.28 ~ 2.3 cm, one leg
and
2.3 + 1 = 3.3 cm, the other leg
:
:
Check this on your calc: enter results 3.99 ~ 4
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