# Minimizing the Length of a Fold: Solving a Calculus Problem

• heather_k2007
In summary, the problem is to determine the best way to fold a piece of paper measuring 12 in. by 8 in. in order to minimize the length of the fold. The solution involves using similar triangles and the Pythagorean Theorem. The length of the crease can be represented by the hypotenuse of a triangle, with the bottom edge and vertical edge being the other sides. The sum of the vertical and horizontal sides is 12 inches. Through the use of these equations, the optimal value for x can be determined.
heather_k2007

## Homework Statement

The upper right-hand corner of a piece of paper, 12 in. by 8 in. is folded over to the bottom edge. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize y?

## Homework Equations

I know I need to use similar triangles and the Pythagorean Theorem (a^2+b^2=c^2) but I'm not sure of how to start the problem

## The Attempt at a Solution

You have to be more specif as for what you mean by the "length". There could be many interpretations.

the length of the crease.

Last edited:
Ok I get it. Well, say the hypotenuse of the triangle is y. The side along the bottom edge is x. The side along the vertical edge is z. Are you aware that

y + z = 12

?

Last edited:
oh okay. i get that.

i actually think i have it now. Thank you very much for your help!

## 1. What is a calculus problem?

A calculus problem is a mathematical problem that involves the use of calculus, a branch of mathematics that deals with the study of continuous change. It typically involves finding the rate of change, the slope of a curve, or the area under a curve.

## 2. Why are calculus problems considered difficult?

Calculus problems are considered difficult because they require a strong understanding of mathematical concepts and techniques. They also often involve complex equations and require multiple steps to solve.

## 3. How do I approach solving a calculus problem?

When approaching a calculus problem, it is important to first identify the given information and what is being asked. Then, use your knowledge of calculus concepts and techniques to solve the problem step by step. It may also be helpful to draw a diagram or graph to visualize the problem.

## 4. What are some common mistakes to avoid when solving a calculus problem?

Some common mistakes to avoid when solving a calculus problem include not understanding the given information, using incorrect formulas or techniques, and making arithmetic errors. It is important to carefully read and understand the problem before attempting to solve it, and to double-check your work for accuracy.

## 5. How can I improve my skills in solving calculus problems?

The best way to improve your skills in solving calculus problems is through practice. Work on a variety of problems to become familiar with different types of questions and techniques. It can also be helpful to seek additional resources, such as textbooks or online tutorials, to deepen your understanding of calculus concepts and methods.

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