Question

A construction company builds a flight of stairs. the end face of each step is in the shape of an isosceles right triangle. if the perimeter around each triangular face is 34 inches, what is the height of each step?

Answer 1

To determine the height of each step for the stair with an isosceles right triangular face and a perimeter of 34 inches, solve the equation 34 = 2h + h√2 where 'h' represents the height.

Step-by-step explanation:

To calculate the height of each step in the isosceles right triangular face with a perimeter of 34 inches, recall that in an isosceles right triangle, the two equal sides (legs) are both equal to the height of the step. Let ‘h’ represent the height of the step. The hypotenuse (‘l’) can be calculated using the Pythagorean theorem where l = √h² + h², simplifying to l = h√2. The perimeter (P) of the triangle is the sum of its sides: P = h + h + l which leads to 34 = 2h + h√2. To find the height, solve for ‘h’ in this equation.

Steps to Solve for Height:

Let h represent the height of the step

1. Use the Pythagorean theorem to find the expression for the hypotenuse of an isosceles right triangle, l = h√2
2. Write the perimeter equation: 34 = 2h + h√2
3. Solve for ‘h’ to find the height

After calculating, the height of each step can be determined, providing the necessary measurement for the construction company.