SOLUTION: a right triangle has an area of 10 square inches. The square of the hypotenuse is 41. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

Question 473606: a right triangle has an area of 10 square inches. The square of the hypotenuse is 41. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a right triangle has an area of 10 square inches. The square of the hypotenuse is 41. Find the lengths of the legs of the triangle. Round your answer to the nearest inch.
:
let a = one leg of the triangle
let b = the other leg
:
Write an equation for the area
*a*b = 10
multiply both sides by 2
a * b = 20
a =
:
"The square of the hypotenuse is 41."; therefore:
a^2 + b^2 = 41
replace a with
+ b^2 = 41
+ b^2 = 41
multiply by b^2, result
400 + b^4 = 41b^2
arrange as a quadratic equation
b^4 - 41b^2 + 400 = 0
This factors to
(b^2-16)(b^2-25) = 0
two solutions
b^2 = 16
b = 4
and
b^2 = 25
b = 5
:
you can see when b = 4, a = 5, and when b = 5, a = 4
:
:
Check the solutions by finding the area and the hypotenuse with these values
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