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

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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)
48m%5E2=%281%2F2%29%28x%5E2%2B2x%29 Multiply each side by 2.
96m%5E2=x%5E2%2B2x+Subtract+96m%5E2+from+each+side.%0D%0A%7B%7B%7B0=x%5E2%2B2x-96m%5E2
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-96+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A-96=388.

Discriminant d=388 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+388+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+388+%29%29%2F2%5C1+=+8.8488578017961
x%5B2%5D+=+%28-%282%29-sqrt%28+388+%29%29%2F2%5C1+=+-10.8488578017961

Quadratic expression 1x%5E2%2B2x%2B-96 can be factored:
1x%5E2%2B2x%2B-96+=+1%28x-8.8488578017961%29%2A%28x--10.8488578017961%29
Again, the answer is: 8.8488578017961, -10.8488578017961. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-96+%29

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