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

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) (Show Source): You can put this solution on YOUR website!
-->
and as , as you said,
<--> <--> .
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
.
Since we need a positive , .
So, .

Accrording to the Pythagorean theorem, , so
.
So, .
Side (the hypotenuse of the right triangle) measures .
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