Question

Corner of a rectangular piece of paper of width 8 inches is folded over so that it coincides with point on the opposite side. If inches, find the length in inches of fold .

Answer 1

The length of the fold is approximately 13.86 inches

Explanation:

The width of the rectangular piece of paper is 8 inches. One corner of the paper is folded over to coincide with a point on the opposite side. We need to find the length of the fold in inches.

To solve this problem, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the folded portion of the paper creates a right triangle. Let's call the length of the fold "x". The width of the paper is 8 inches. The folded portion of the paper forms one side of the right triangle, with length x. The other two sides of the right triangle are the width of the paper, which is 8 inches, and the length of the paper, which is unknown.

Using the Pythagorean Theorem, we can write the equation:

x^2 + 8^2 = (length of the paper)^2

Simplifying the equation:

x^2 + 64 = (length of the paper)^2

Now we need to find the length of the paper. We know that the length of the paper is 8 inches longer than the width, so we can write:

length of the paper = 8 + 8 = 16 inches

Substituting this value into the equation:

x^2 + 64 = 16^2

x^2 + 64 = 256

Solving for x:

x^2 = 256 - 64

x^2 = 192

x ≈ √192

x ≈ 13.86 inches

Therefore, the length of the fold is approximately 13.86 inches

Answer 2

The length of the fold is 8√2 inches.

How to determine the length of the fold .

When a rectangular piece of paper is folded, a right-angled triangle is formed. The folded part is the hypotenuse, and the width of the paper (8 inches) is one leg of the triangle. The other leg is the length of the fold.

Using the Pythagorean Theorem

a²+ b² = c²

where

c is the hypotenuse,

a and b are the legs:

8²+ b² = c²

64 + b² = c²

Now, since the paper is folded, the length of the fold b is also the width of the paper. The width is 8 inches.

64 + 8² = c²

64 + 64 = c²

128 = c²

c = √128

c = 8√2

So, the length of the fold is 8√2 inches.