SOLUTION: in a right-angled triangle one right-angled side is 2m longer than the other one. Calculate the length of the two right-angled sides if the area is 48m^2

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Question 952084: in a right-angled triangle one right-angled side is 2m longer than the other one. Calculate the length of the two right-angled sides if the area is 48m^2
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
x=shorter leg (height); x+2m=longer leg (base); Area=1/2(base)(height)
A=(1/2)(x)(x+2)
Multiply each side by 2.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=388 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8.8488578017961, -10.8488578017961. Here's your graph:

ANSWER 1: The shorter side is 8.85 meters.
x+2=8.85+2=10.85 ANSWER 2: The longer side is 10.85 meters.
CHECK:
a=1/2(b)(h)
48 sq m=(1/2)(10.85 m)(8.85m)
48 sq m=48 sq m
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