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

Question 218772: if a right triangle has a area 180cm^(2) and hypotenuse 41 cm, find the length of the two legs
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
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.

For Step-By-Step videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry please visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.

Respectfully,
Dr J

http://www.FreedomUniversity.TV
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