Question

An order was placed at a custom design store for a trapezoidal flag. The customer left instructions for the top base to be 10 inches less than the height. The design team came up with a flag design to the customer's specifications with an area given by the equation below, where h is the height S = 3h2 - 3h .Which of the following best describes the bottom base of the flag?

A. The bottom base is 4 inches longer than 5 times the height.
B. The bottom base is 16 inches shorter than 5 times the height.
C. The bottom base is 13 inches shorter than 2 times the height.
D. The bottom base is 7 inches longer than 2 times the height​

Answer 1

The bottom base of the trapezoidal flag is 16 inches shorter than 5 times the height, which is option B according to the area formula provided and the formula for the area of a trapezoid.

Step-by-step explanation:

To determine the bottom base of a trapezoidal flag based on the given area formula S = 3h2 - 3h, we have to recall the formula for the area of a trapezoid, which is S = (1/2) * (a + b) * h, where 'h' is the height, 'a' is the top base, and 'b' is the bottom base.

Given that the top base (a) is 10 inches less than the height, we can express it as a = h - 10. Substituting the area of a trapezoid with the provided equation 3h2 - 3h, we get:

3h2 - 3h = (1/2) * (h - 10 + b) * h

Solving for 'b' (the bottom base), we multiply both sides by 2/h:

2 * (3h2 - 3h) / h = h - 10 + b

6h - 6 = h - 10 + b

Solving for 'b', we get:

b = 5h - 16

Thus, the bottom base is 16 inches shorter than 5 times the height, which coincides with choice B.