SOLUTION: The area of a triangular sheet of paper is 185 square inches. One side of the triangle is 7 inches more than three times the length of the altitude to that side. Find the length of

Algebra.Com
Question 951622: The area of a triangular sheet of paper is 185 square inches. One side of the triangle is 7 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.
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
b=side; h=altitude; A=Area=(1/2)b*h
A=(1/2)b*h
185 sq in=(1/2)(3h+7in)(h) Multiply each side by 2.
Subtract 370 sq in from each side.
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=4489 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 10, -12.3333333333333. Here's your graph:

ANSWER 1: Length of the altitude is 10 inches
b=3h+7in=3(10in)+7in=37 in ANSWER 2: The length of the side is 37 inches.
CHECK:
Area=1/2bh=1/2(37 in)(10 in)
185 sq in=1/2(370 sq in)
185 sq in=185 sq in
RELATED QUESTIONS

The area of a triangular sheet of paper is 28 square inches. One side of the triangle is... (answered by mananth)
Please help me if you can. The area of a triangular sheet of paper is 28 square... (answered by scott8148)
The area of a triangular sheet of paper is 190 square inches. One side of the triangle is (answered by mananth,edjones)
"The area of a triangular sheet of paper is 28 square inches. One side of the triangle is (answered by mananth)
the area of a triangular sheet of paper is 13 square inches. one side of the triangle is... (answered by solver91311,Gogonati)
The area of a triangular sheet of paper is 27 square inches. One side of the triangle is... (answered by josgarithmetic)
A triangular sheet of paper is 28 square inches, one side of the triangle is 2 inches... (answered by AnlytcPhil,venugopalramana)
The length of a sheet of paper is 14 inches more than its width and its area is 912... (answered by Alan3354)
The area of a triangular sheet of paper is 18 square inches. One side of the triangle is... (answered by solver91311,scott8148)