SOLUTION: Mark wants to make a unique triangular design that will cover the vacant space of his bedroom wall. His mother, Annie, suggests a right triangle design will be a perfect fit. She s

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Mark wants to make a unique triangular design that will cover the vacant space of his bedroom wall. His mother, Annie, suggests a right triangle design will be a perfect fit. She s      Log On


   

Question 1185814: Mark wants to make a unique triangular design that will cover the vacant space of his bedroom wall. His mother, Annie, suggests a right triangle design will be a perfect fit. She suggests that hypotenuse should be at least 15ft and one leg is 3ft shorter than the other. What is the length of the longer leg? With Solution.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
.

(9, 12, 15)  is the  3-4-5  right angled triangle.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The statement of the problem as shown is defective; there are an infinite number of right triangles that satisfy the given requirements.

Let the longer leg be x; then the shorter leg is x-3. The hypotenuse needs to be at least 15.

x%5E2%2B%28x-3%29%5E2%3E=15%5E2
x%5E2%2Bx%5E2-6x%2B9%3E=225
2x%5E2-6x-216%3E=0
x%5E2-3x-108%3E=0
%28x-12%29%28x%2B9%29%3E=0

x is greater than 12 or x is less than -9. Obviously the negative number makes no sense.

ANSWER: the longer leg can be ANY length greater than 12 feet.