SOLUTION: The hypotenuse of a right triangle is 12cm longer than the shortest side, and 6cm longer than the remaining side. Find the dimensions of the triangle

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Question 954664: The hypotenuse of a right triangle is 12cm longer than the shortest side, and 6cm longer than the remaining side. Find the dimensions of the triangle
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
c=hypotenuse; a=shortest leg=c-12cm; b=longer leg=c-6cm
Substitute for a and b.


Subtract from each side.
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=576 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 30, 6. Here's your graph:

Possible solutions are 30 and 6 Since a=c-12, 6 doesn't work.
c=30 cm
ANSWER 1: The hypotenuse is 30 cm.
a=c-12cm=30-12cm=18cm
ANSWER 2: The shortest leg is 18 cm.
b=c-6cm=30-6cm=24cm
ANSWER 3: The longer leg is 24 cm.
CHECK:
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