Solve.
-A triangular piece of glass is being cut so that the height of the triangle is 4 inches shorter than twice the base. If the area of the triangle is 24 square inches, how long is the height of the triangle?
A)10 in.
B)12 in.
C)8 in.
D)6 in.

Question

Quizplus · Accepted Answer

Let the length of the base of the triangle be x.
Then, the height of the triangle would be 2x - 4 (since it is 4 inches shorter than twice the base).
The area of a triangle is given by the formula (1/2)base*height.
So, we can set up an equation:
(1/2)*x*(2x-4) = 24
Simplifying this equation, we get:
x*(2x-4) = 48
2x^2 - 4x - 48 = 0
x^2 - 2x - 24 = 0
(x-6)(x+4) = 0
x = 6 or x = -4 (we can discard the negative value)

Therefore, the length of the base is 6 inches.
The height of the triangle is:
2x - 4 = 2(6) - 4 = 8 inches.

Thus, the answer is C (8 in.)

Solve. -A Triangular Piece of Glass Is Being Cut So That