Question

the dimensions of a rectangular piece of paper are 20.8 cm and 30.6 cm. jon folded the paper along its diagonal. what is the length of the diagonal in inches?

Explanation:

Step1: Recall the Pythagorean theorem for a rectangle

For a rectangle with length \( l \) and width \( w \), the length of the diagonal \( d \) is given by the Pythagorean theorem: \( d=\sqrt{l^{2}+w^{2}} \). Here, \( l = 30.6\space\text{cm} \) and \( w=20.8\space\text{cm} \).

Step2: Calculate the diagonal in centimeters

First, calculate \( l^{2} \) and \( w^{2} \):
\( l^{2}=(30.6)^{2}=30.6\times30.6 = 936.36 \)
\( w^{2}=(20.8)^{2}=20.8\times20.8=432.64 \)
Then, \( l^{2}+w^{2}=936.36 + 432.64=1369 \)
So, \( d=\sqrt{1369}=37\space\text{cm} \) (since \( 37\times37 = 1369 \))

Step3: Convert centimeters to inches

We know that \( 1\space\text{inch}\approx2.54\space\text{cm} \). To convert centimeters to inches, we use the formula \( \text{inches}=\frac{\text{centimeters}}{2.54} \)
So, \( \text{Length in inches}=\frac{37}{2.54}\approx14.57\space\text{inches} \) (or we can also note that since \( 37\div2.54\approx14.57 \), and also, we can recall that \( 1\space\text{cm}=\frac{1}{2.54}\space\text{inch} \), so \( 37\space\text{cm}=37\times\frac{1}{2.54}\space\text{inch}\approx14.57\space\text{inch} \))

Answer:

The length of the diagonal is approximately \( \boldsymbol{14.57} \) inches (or if we consider the exact value from the square root and conversion, we can also note that since \( 37\space\text{cm}\) is the diagonal, and \( 37\div2.54\approx14.57 \)). If we want a more precise or rounded value, we can say approximately 14.6 inches or 14.57 inches. The exact value after calculation is approximately \( 14.57 \) inches.