SOLUTION: I have gone over this several times but I get so confused! Can you help? The hypotenuse of a right triangle is 32 cm more than one of the legs. If the other leg is 120 cm, how lon

Algebra ->  Pythagorean-theorem -> SOLUTION: I have gone over this several times but I get so confused! Can you help? The hypotenuse of a right triangle is 32 cm more than one of the legs. If the other leg is 120 cm, how lon      Log On


   

Question 788833: I have gone over this several times but I get so confused! Can you help? The hypotenuse of a right triangle is 32 cm more than one of the legs. If the other leg is 120 cm, how long is the hypotenuse?
Found 2 solutions by josgarithmetic, ankor@dixie-net.com:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Legs x and y. Hypotenuse h.
x=120
y=?
h=32+y

Pythagorean Theorem: h%5E2=x%5E2%2By%5E2
%2832%2By%29%5E2=120%5E2%2By%5E2
32%5E2%2B2%2A32y%2By%5E2=120%5E2%2By%5E2
See y^2 as term on both sides of the equation. Subtract y^2 from both sides.
32%5E2%2B2%2A32y=120%5E2
Simplify and solve for y.
64y%2B32%5E2=120%5E2
64y=120%5E2-32%5E2
y=%28120%2B32%29%28120-32%29%2F64 ------because expression shows difference of two squares.
y=%28152%29%2888%29%2F64
Keep simplifying,

highlight%28y=19%2A11%29
That is the leg, y, in factored form. Just use it in computed form to help compute the value of h.

highlight%28h=32%2B19%2A11%29

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 32 cm more than one of the legs.
If the other leg is 120 cm, how long is the hypotenuse?
:
Let c = the length of the hypotenuse
then
(c-32) = one leg
:
Using a^2 + b^2 = c^2, we have:
120^2 + (c-32)^2 = c^2
FOIL (c-32)(c-32), do the math
14400 + c^2 - 64c + 1024 = c^2
Subtract c^2 from both sides
15424 - 64c = 0
15424 = 64c
c = 15424/64
c = 241 cm is the hypotenuse
:
:
Check this on your calc
other leg 241-32 = 209
Enter sqrt%28120%5E2%2B209%5E2%29 results: 241, confirms our solution