Question

A state law prohibits triangular signs with areas exceeding 30 ft². If someone orders a triangular sign with a 12-ft base, how tall can the sign be? The sign cannot be taller than ____.

a) 15 ft
b) 20 ft
c) 25 ft
d) 30 ft

Answer 1

To determine the maximum height of the triangular sign with a 12-ft base that does not exceed a 30 ft² area, the formula for the area of a triangle is used, and the calculation shows that the height cannot exceed 5 feet.

Step-by-step explanation:

The question involves solving a problem related to the area of a triangle to comply with a state law. To find the maximum allowable height of a triangular sign with a 12-ft base, we use the formula for the area of a triangle: Area = 1/2 × base × height. Given that the maximum area is 30 ft², we can set up the equation:

30 = 1/2 × 12 × height

The resulting equation can then be simplified to find the height:

30 = 6 × height

height = 30 / 6

height = 5 ft

This solution indicates that the sign's height cannot exceed 5 feet to satisfy the state law.