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2. A piece of paper is 22 by 28 centimeters. Use the Pythagorean theorem to determine the length of the diagonal of the paper. Show your work.

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GinnyAnsweridn
To determine the length of the diagonal of a piece of paper that is 22 by 28 centimeters, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides.

Let's denote the length as [tex]\( a \)[/tex] and the width as [tex]\( b \)[/tex].
- [tex]\( a = 22 \)[/tex] cm
- [tex]\( b = 28 \)[/tex] cm

The diagonal [tex]\( d \)[/tex] can be found using the formula:
[tex]\[ d = \sqrt{a^2 + b^2} \][/tex]

### Step-by-Step Solution:

1. Square the length and the width:

[tex]\[ 22^2 = 484 \][/tex]

[tex]\[ 28^2 = 784 \][/tex]

2. Add the squared values together:

[tex]\[ 484 + 784 = 1268 \][/tex]

3. Take the square root of the sum to find the diagonal:

[tex]\[ d = \sqrt{1268} \approx 35.608987629529715 \][/tex]

So, the length of the diagonal of the paper is approximately [tex]\( 35.61 \)[/tex] centimeters.
Fadinglightidn
To find the diagonal length via the Pythagorean Theorem, you’d first need to plug in the values.

A^2 + B^2 = C^2

22^2 + 28^2 = C^2

The reason we put those two values for A and B, is because we know that C is the largest value, and the hypotenuse of a triangle is always the longest side.

Which from there, we have to square all the values to get,

484 + 784 = C^2

Which when you add common terms becomes,

1268 = C^2

From there we square root both sides, to finally get,

C ≈ 35.61

Or sqrt1268

Which cannot be rationalized I believe
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