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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

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) About Me  (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:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation: a=2, b=2, c=-15
x+=+%28-2+%2B-+sqrt%282%5E2-4%2A2%2A-15+%29%29%2F%282%2A2%29+
:
x+=+%28-2+%2B-+sqrt%284-%28-120%29+%29%29%2F4+
:
x+=+%28-2+%2B-+sqrt%28124%29%29%2F4+
the positive solution is all we want here
x+=+%28-2+%2B+11.1355%29%2F4+
x = 9.1355%2F4
x = 2.28 ~ 2.3 cm, one leg
and
2.3 + 1 = 3.3 cm, the other leg
:
:
Check this on your calc: enter sqrt%282.28%5E2+%2B+3.28%5E2%29 results 3.99 ~ 4