Question

A company makes traffic signs.One of their signs can be modeled by an equilateral triangle with a perimeter of 144 inches. The company makes a similar sign with perimeter that is 1.25 times the one shown. What is the height in inches of the larger sign?

Answer 1

To find the height of the larger sign, determine the scale factor between the two signs and use the formula for the height of an equilateral triangle.

Step-by-step explanation:

To find the height of the larger sign, we need to determine the scale factor between the two signs. The perimeter of the original sign is 144 inches, and the new sign has a perimeter that is 1.25 times the original. This means the perimeter of the new sign is 144 x 1.25 = 180 inches.

Since the original sign is an equilateral triangle, each side has a length of 144/3 = 48 inches. The larger sign will have sides that are 180/3 = 60 inches in length.

Since the larger sign is also an equilateral triangle, we can use the formula h = (√3/2) x s, where h is the height and s is the length of a side. Therefore, the height of the larger sign is h = (√3/2) x 60 = 51.96 inches (rounded to two decimal places).

Answer 2

The perimeter of the larger sign : 144*1,25= 180 inches

Side of the triangle= 180/3= 60 inches

square of the height= 60^(2) - 30^(2)= 2700 ( Pythagoras' theorem)

height= square root ( 2700)= 51,96

Step-by-step explanation: