SOLUTION: Write a quadratic equation in standard form with the given solutions. The hypotenuse of a right triangle measures 8 in. More than one leg and 3 in. More than the other leg. Find

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Write a quadratic equation in standard form with the given solutions. The hypotenuse of a right triangle measures 8 in. More than one leg and 3 in. More than the other leg. Find      Log On


   

Question 1029997: Write a quadratic equation in standard form with the given solutions.
The hypotenuse of a right triangle measures 8 in. More than one leg and 3 in. More than the other leg. Find the lengths of the sides of the triangle ( to the nearest tenth of an inch).
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Hypotenuse = x
leg 1 = x-8
leg 2 = x-3
%28x-8%29%5E2%2B%28x-3%29%5E2=x%5E2
+x%5E2-16x%2B64%2Bx%5E2-6x%2B9=x%5E2
x%5E2-22x%2B73=0
Find the roots of the equation by quadratic formula

a= 1 b= -22 c= 73

b^2-4ac= 484 - 292
b^2-4ac= 192 sqrt%28%09192%09%29= 13.86
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 22 + 13.86 )/ 2
x1= 17.93
x2=( 22 -13.86 ) / 2
x2= 4.07
Since one leg is 8 cm less than the hypotenuse
x= 17.93
leg 1 = 17.93-8 = 9.93
leg 2 = 17.93 -3= 14.93
Check
9.93^2+14.93^2=321.5098
17.93^2= 321.4849