Question
the diagonal of a rectangular tabletop measures 52 in. if the width is 20 in. what is the length of the tabletop rounded to the nearest inche
Answers
GPT-4o mini
To find the length of the rectangular tabletop, we can use the Pythagorean theorem, which states that in a right 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 (the width and the length).
Let \( L \) be the length of the tabletop. According to the Pythagorean theorem:
\[
d^2 = w^2 + L^2
\]
where:
- \( d = 52 \) in (the diagonal),
- \( w = 20 \) in (the width),
- \( L \) is the length we are trying to find.
Substituting the known values into the equation:
\[
52^2 = 20^2 + L^2
\]
Calculating the squares:
\[
2704 = 400 + L^2
\]
Next, subtract \( 400 \) from both sides to solve for \( L^2 \):
\[
2704 - 400 = L^2
\]
\[
2304 = L^2
\]
Now, take the square root of both sides to find \( L \):
\[
L = \sqrt{2304}
\]
Calculating the square root:
\[
L = 48
\]
Therefore, the length of the tabletop is \( 48 \) inches when rounded to the nearest inch.
Let \( L \) be the length of the tabletop. According to the Pythagorean theorem:
\[
d^2 = w^2 + L^2
\]
where:
- \( d = 52 \) in (the diagonal),
- \( w = 20 \) in (the width),
- \( L \) is the length we are trying to find.
Substituting the known values into the equation:
\[
52^2 = 20^2 + L^2
\]
Calculating the squares:
\[
2704 = 400 + L^2
\]
Next, subtract \( 400 \) from both sides to solve for \( L^2 \):
\[
2704 - 400 = L^2
\]
\[
2304 = L^2
\]
Now, take the square root of both sides to find \( L \):
\[
L = \sqrt{2304}
\]
Calculating the square root:
\[
L = 48
\]
Therefore, the length of the tabletop is \( 48 \) inches when rounded to the nearest inch.