A shopkeeper is making a triangular sign for his store front, but he must keep the sign under 20 square feet to adhere to the zoning laws. If the base of the sign is 20 feet, what is the maximum height of the triangular sign?
Area of triangle = (1/2)base x height
(1/2(20)(height) < 20
solve for height
To find the maximum height of the triangular sign, we need to calculate the area of the triangle first. The formula to find the area of a triangle is:
Area = (base * height) / 2
Given that the base of the sign is 20 feet, and the area needs to be less than or equal to 20 square feet, we can rearrange the formula as follows:
20 ≤ (20 * height) / 2
Now, let's solve for the maximum height.
Multiply both sides of the inequality by 2:
40 ≤ 20 * height
Divide both sides of the equation by 20:
2 ≤ height
Therefore, the maximum height of the triangular sign is 2 feet.