The area of a triangular sheet of paper is 116 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 4 inches, a side of 29 inches long.
B) An altitude of 8 inches, a side of 29 inches long.
C) An altitude of 29 inches, a side of 8 inches long.

Question

Quizplus · Accepted Answer

Let the altitude be x and the length of the side be y. Then we have the equation "xy = 116" (since the area is 116 square inches). We also know that "y = 3x + 5" (since one side is 5 more than three times the altitude). Substituting y in terms of x into the first equation, we get:

x(3x + 5) = 116
3x^2 + 5x - 116 = 0

Solving for x using the quadratic formula, we get x = 8 or x = -4/3 (we ignore the negative solution since we're dealing with lengths). Plugging x=8 into y=3x+5, we get y=29. Therefore, the altitude is 8 inches and the length of the side is 29 inches.

The Area of a Triangular Sheet of Paper Is 116