The area of a triangular sheet of paper is 11 square inches. One side of the triangle is 5 inches more than three times the length of the altitude to that side. Find the length of that side and the altitude to the side.
A)an altitude of 11 inches, a side of 21 inches long
B)an altitude of 2 inches, a side of 11 inches long
C)an altitude of 1 inches, a side of 11 inches long
D)an altitude of 11 inches, a side of 2 inches long
E)none of these

Question

Quizplus · Accepted Answer

Let the altitude be x and the length of the side be y. We know that xy/2 = 11, so xy = 22. We also know that y = 3x + 5. Substituting y in terms of x, we get (3x + 5)x = 22. Simplifying this gives us 3x^2 + 5x - 22 = 0. Factoring this equation or using the quadratic formula gives us x = 2 or x = -11/3. Since the altitude cannot be negative, we take x = 2. Plugging this back into y = 3x + 5 gives us y = 11. Therefore, the altitude is 2 inches and the side is 11 inches long, which is option B.

The Area of a Triangular Sheet of Paper Is 11