Question

You are given a rectangular piece of paper that has length

x=30.2 cm and height
y=11 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.

Maximum Area =
165.11 cm² (when the paper is folded in half along its length)
Minimum Area=
90.66 cm² (when the paper is folded in half along its width)

Answer 1

The maximum area of the triangle formed by folding the paper in half along its length is 82.6 cm², while the minimum area of the triangle formed by folding the paper in half along its width is also 82.6 cm².

Step-by-step explanation:

To determine the maximum and minimum area of a triangle that can be formed by folding the given rectangular piece of paper, we need to consider two different scenarios:

1. Maximum Area: Folding the paper in half along its length:

• The length of the folded paper becomes 30.2 cm / 2 = 15.1 cm.
• The height of the folded paper remains the same at 11 cm.
• Using the formula for the area of a triangle, the maximum area is 1/2 x base x height = 1/2 x 15.1 cm x 11 cm = 82.6 cm².

Minimum Area: Folding the paper in half along its width:

• The length of the folded paper remains the same at 30.2 cm.
• The height of the folded paper becomes 11 cm / 2 = 5.5 cm.
• Using the formula for the area of a triangle, the minimum area is 1/2 x base x height = 1/2 x 30.2 cm x 5.5 cm = 82.6 cm².