# A fold is formed on a #20 cm × 30 cm# rectangular sheet of paper running from the short side to the long side by placing a corner over the long side. Find the minimum possible length of the fold?

# L = 15sqrt(3) ~~ 25.98 \ cm#

Let us set up the following variables:

# {

```
(L, "Length of the fold", cm),
(x, "DE", cm),
(theta, "Angle " hat(DGE), "radians")
```

:} #

Now:

Using the sum of angle formula:

we have:

Using the identity:

we have:

At a critical point this derivative vanishes, and so:

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The minimum possible length of the fold on a 20 cm × 30 cm rectangular sheet of paper formed by placing a corner over the long side is 25 cm.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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