Question

(16 points) You are given a rectangular piece of paper that has length x=28.2 cm and height y=22 cm. The lower right corner is to be folded to the top edge forming a triangle as shown. Determine the maximum and minimum area of a triangle that can be constructed.

Answer 1

The maximum area of the triangle is 311.4 cm² and the minimum area is 155.1 cm².

Step-by-step explanation:

The area of a triangle can be calculated using the formula: A = 1/2 * base * height.

In this case, the length of the rectangular paper is the base (x), which is 28.2 cm, and the height of the paper is the height of the triangle (y), which is 22 cm.

To find the maximum area, we need to fold the lower right corner to the top edge in such a way that the folded side is the hypotenuse of the triangle. This will create a right-angled triangle with maximum area. By calculating the area using the formula, we get:

Maximum Area: A = 1/2 * 22 cm * 28.2 cm = 311.4 cm²

To find the minimum area, we need to fold the paper in a way that the folded side is the base of the triangle. This will create a right-angled triangle with minimum area. By calculating the area using the formula, we get:

Minimum Area: A = 1/2 * 22 cm * 14.1 cm = 155.1 cm²