Question

An envelope measures 33 centimeters by 44 centimeters. A pencil is placed in the envelope at a diagonal. What is the maximum possible length of the pencil?

Answer 1

The maximum possible length of the pencil is 55 centimeters (cm).

Explanation:

We know that the Pythagorean Theorem states that a² + b² = c² in a right triangle.

a = the altitude (the vertical line of a right triangle)

b= the base (the horizontal line of a right triangle)

c= the hypotenuse (the diagonal line of a right triangle)

1. substitute 33 for a and 44 for b

33² + 44² = c²

2. simplify the expression

1089 + 1936 = c²

3. combine like terms

3025 = c²

4. square root both sides

√3025 = √c²

55 = c

c = 55

This means that the maximum possible length of the pencil is 55 centimeters (cm).

Answer 2

We can use the Pythagorean theorem to solve this problem. If we consider the diagonal of the envelope to be the hypotenuse of a right triangle, then the length and width of the envelope are the legs of the triangle. Let d be the length of the pencil.

We can write the Pythagorean theorem as:

d^2 = 33^2 + 44^2

Simplifying, we get:

d^2 = 1089 + 1936

d^2 = 3025

Taking the square root of both sides, we get:

d = 55

Therefore, the maximum possible length of the pencil is 55 centimeters.