SOLUTION: If i know that the lentgh of the hypotenuse is 10cm and area of right triangle is 24 cm^2 How do i calculate the other two sides?

Algebra ->  Pythagorean-theorem -> SOLUTION: If i know that the lentgh of the hypotenuse is 10cm and area of right triangle is 24 cm^2 How do i calculate the other two sides?      Log On


   

Question 829508: If i know that the lentgh of the hypotenuse is 10cm and area of right triangle is 24 cm^2
How do i calculate the other two sides?
Found 2 solutions by oscargut, josgarithmetic:
Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
Let b and h the length of the 2 sides
24 = bh/2
and b^2+h^2= 100
If you solve it the lengths are 6 and 8

If you need more help you can contact me at
mthman@gmail.com
Thanks

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You need more data.
So far you have some x and y and hypotenuse=10.
You can say x%5E2%2By%5E2=10%5E2, and this is two unknown variables and one equation.

You also have %281%2F2%29xy=24. Is this enough?

Working with the area, xy=48,
y=48%2Fx.
Substitute into the other equation:
x%5E2%2B%2848%2Fx%29%5E2=100
x%5E4%2B48%5E2=100x%5E2
x^4-100x^2+48^2=0
Try a substitution for this quadratic form, like u=x%5E2, and solve first for u.
-
u%5E2-100u%2B2304=0
Directly use general solution of quadratic formula.
u=%28100%2B-+sqrt%2810000-4%2A%282304%29%29%2F%282%29%29
u=%28100%2B-+sqrt%28784%29%29%2F2
784=4*196=4*4*49=4*4*7*7
u=%28100%2B-+28%29%2F2
u = 36 or u=64
-
Now go back to definition of u and find x. You want only the positive values.
x=sqrt(u), so x=6 or x=8
.
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ANSWER: Side lengths or legs are 6 and 8.
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