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?

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) (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) (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 , and this is two unknown variables and one equation.

You also have . Is this enough?

Working with the area, ,
.
Substitute into the other equation:

x^4-100x^2+48^2=0
Try a substitution for this quadratic form, like , and solve first for u.
-

Directly use general solution of quadratic formula.

784=4*196=4*4*49=4*4*7*7

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 or
.
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ANSWER: Side lengths or legs are 6 and 8.
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