The area of a triangle is 20 square inches. One side of the triangle is 7 inches less than three times the length of the altitude to that side. Find the length of that side.
A) 9 in.
B) 10 in.
C) 6 in.
D) 8 in.

Question

Quizplus · Accepted Answer

Let the altitude to the side be x. Then, the side is 3x - 7. We can use the formula for the area of a triangle to set up an equation:

(1/2)(3x-7)(x) = 20

Multiplying both sides by 2 gives:

(3x-7)(x) = 40

Expanding the left side gives:

3x^2 - 7x = 40

Bringing all terms to one side gives:

3x^2 - 7x - 40 = 0

Factorizing, we get:

(3x + 8)(x - 5) = 0

Since, x cannot be negative or zero, we have:

x = 5

Therefore, the side length is:

3x - 7 = 3(5) - 7 = 8

So, the answer is D, 8 in.

The Area of a Triangle Is 20 Square Inches