SOLUTION: Area of a right triangle is six radical 2 cm² and the length of one leg is radical 12 cm. What is the length of the other leg? What is the length of the hypotenuse?

Algebra ->  Radicals -> SOLUTION: Area of a right triangle is six radical 2 cm² and the length of one leg is radical 12 cm. What is the length of the other leg? What is the length of the hypotenuse?      Log On


   

Question 923749: Area of a right triangle is six radical 2 cm² and the length of one leg is radical 12 cm. What is the length of the other leg? What is the length of the hypotenuse?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
A=6sqrt%282%29cm%5E2=6%2A1.41cm%5E2=>A=8.46cm%5E2
the length of one leg is a=sqrt%2812%29cm=>highlight%28a=3.464cm%29
A=a%2Ab%2F2 where base a=one_leg and height b=other_leg
8.46cm%5E2=%283.464cm%2Ab%29%2F2
2%2A8.46cm%5E2=3.464cm%2Ab
16.92cm%5E2=3.464cm%2Ab

16.92cm%5E2%2F3.464cm=b
b=4.884526558891455cm
highlight%28b=4.89cm%29%29-the length of the other leg
What is the length of the hypotenuse c?
c%5E2=a%5E2%2Bb%5E2
c%5E2=%283.464cm%29%5E2%2B%284.89cm%29%5E2
c%5E2=11.999296cm2%2B23.9121cm%5E2
c%5E2=35.911cm%5E2
c=sqrt%2835.9cm%5E2%29
c=5.99166cm
highlight%28c=5.99cm%29