Question

Steve has an isosceles triangle with base $8$ inches and height $10$ inches. he wants to cut it into eight pieces that have equal areas, as shown below. to the nearest hundredth of an inch what is the number of inches in the greatest perimeter among the eight pieces?

Answer 1

To find the number of inches in the greatest perimeter among the eight pieces, divide the area of the isosceles triangle by 8 to get the area of each piece. Then, calculate the perimeter of each piece by doubling the sum of the base and height. The greatest perimeter among the eight pieces is approximately 26 inches.

Step-by-step explanation:

To find the number of inches in the greatest perimeter among the eight pieces, first we need to determine the area of the isosceles triangle. The area of a triangle is given by the formula 1/2 × base × height. Plugging in the values from the question, the area = 1/2 × 8 × 10 = 40 square inches.

Since we want to cut the triangle into eight pieces with equal areas, we divide the area of the triangle by 8 to get the area of each piece. The area of each piece = 40 / 8 = 5 square inches.

Now, let's consider the pieces. If we divide the triangle horizontally into two equal parts, each part would have a base of 8 inches and a height of 5 inches. Therefore, the perimeter of each piece, which is twice the sum of the base and height, would be 2 × (8 + 5) = 26 inches.

Therefore, the number of inches in the greatest perimeter among the eight pieces is approximately 26 inches.