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If a right triangle has a area 180cm^(2) and hypotenuse 41 cm, find the length of the two legs.
Step 1. The Area
where a and b are legs of the triangle.
Step 2. The Pythagorean Theorem is the sum of the squares of the legs (a and b) is equal to the square of the hypotenuse c
Step 3. Multiply by a^2 to both sides of the equation to get rid of denominator and c=41.
Step 4. Let x=a^2 to simplify equation as a quadratic
|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=2307361 is greater than zero. That means that there are two solutions: .
Quadratic expression can be factored:
Again, the answer is: 1600, 81.
Here's your graph:
Step 5. Taking the square root yields a=40 and a=9.
Then b is
Step 6. ANSWER: The legs of the right triangle are 9 cm and 40 cm.
I hope the above steps and explanation were helpful.
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