# SOLUTION: if a right triangle has a area 180cm^(2) and hypotenuse 41 cm, find the length of the two legs

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Question 218772: if a right triangle has a area 180cm^(2) and hypotenuse 41 cm, find the length of the two legs
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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:

We have and , then and

Step 5. Taking the square root yields a=40 and a=9.

Then b is or .

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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