Question

A square piece of sheet metal is to be used to make a stop sign. each side of the sheet metal is 50cm long. A triangle will be cut off each corner, leaving a regular octagon. which pair of equations can be used to calculate the length of each side of the octagon

Answer 1

To find the length of each side of the octagon, use the Pythagorean theorem to solve for the length of one of the legs of a right triangle.

Step-by-step explanation:

To calculate the length of each side of the regular octagon, we need to find the length of the triangle that is cut off from each corner of the square sheet metal.

Since the square has side length of 50 cm, half the length of the triangle's base is also 50 cm. By drawing the altitude of the triangle, we create two right triangles.

We can use the Pythagorean theorem to find the length of one of the legs of the right triangle, which will be the length of each side of the octagon. The equation can be set up as follows:

Leg length of right triangle = √(50^2 - (50/2)^2)

Solving this equation will give us the length of each side of the octagon.