SOLUTION: A right triangle has an area of 84 ft^2 and a hypotenuse that is 25 ft long. What are the the lengths of its other two sides?
Algebra ->
Triangles
-> SOLUTION: A right triangle has an area of 84 ft^2 and a hypotenuse that is 25 ft long. What are the the lengths of its other two sides?
Log On
Question 368910: A right triangle has an area of 84 ft^2 and a hypotenuse that is 25 ft long. What are the the lengths of its other two sides? Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! hypotenuse = 25
let one leg be x
other leg = sqrt(25^2-x^2)
...
Area = 1/2 * x * sqrt(25^2-x^2)
84= x/2*sqrt(25^2-x^2)
square both sides
84^2= x^2/4 (25^2-x^2)
4*84^2 = x^2(25^2-x^2)
4*84^2=625x^2-x^4
x^4-625x^2+28224=0
x^4-576x^2-49x^2+28224=0
x^2(x^2-576)-49(x^2-576)=0
(x^2-576)(x^2-49)=0
(x+24)(x-24)(x+7)(x-7)=0
take only the positive values of x
24 &7 are the legs of the triangle..
...
CHECK
24^2+7^2= 25^2
...
m.ananth@hotmail.ca
