SOLUTION: in triangle ABC, a-b=5 and the area is 50 cm squared. If angle C is 90 degrees, find the side length of c. so far, I know that a*b=100 and that a and b are both decimals because

Algebra ->  Equations -> SOLUTION: in triangle ABC, a-b=5 and the area is 50 cm squared. If angle C is 90 degrees, find the side length of c. so far, I know that a*b=100 and that a and b are both decimals because      Log On


   

Question 1033222: in triangle ABC, a-b=5 and the area is 50 cm squared. If angle C is 90 degrees, find the side length of c.
so far, I know that a*b=100 and that a and b are both decimals because no whole numbers that are factors of 100 have a difference of 5.
**the a is the base of the triangle, b is the height, c is the diagonal and the longest side of the triangle. Also, angle C is a right angle, and angles A and B are located on line c***
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
a-b=5 --> a=b%2B5
and as a%2Ab=100 , as you said,
%28b%2B5%29%2Ab=100 <--> b%5E2%2B5b=100 <--> b%5E2%2B5b-100=0 .
That is a quadratic equation.
When you are lucky, you get a quadratic equation that can be solved by factoring.
No such luck in this case, because as you said no whole numbers that are factors of 100 have a difference of 5.
So, we have to solve that equation by completing the square or by using the quadratic formula.
Either way, the solutions are
b=%28-5+%2B-+5sqrt%2817%29%29%2F2=%285%2F2%29%28-1+%2B-+Sqrt%2817%29%29 .
Since we need a positive b , highlight%28b=%28-5+%2B+5sqrt%2817%29%29%2F2=%285%2F2%29%28-1+%2B+sqrt%2817%29%29%29 .
So, .

Accrording to the Pythagorean theorem, c%5E2=a%5E2%2Bb%5E2 , so
.
So, c=sqrt%28%285%2F2%29%5E2%2A6%5E2%29=%285%2F2%29%2A6=highlight%2815%29 .
Side c (the hypotenuse of the right triangle) measures highlight%2815cm%29 .