Question

Use the Pythagorean theroum to find the diagonal length of the bottom of the box with measurements of 24 in 18 in and 16 in

Answer 1

To find the diagonal length of the bottom of the box, we can use the Pythagorean theorem. In this case, the bottom of the box can be considered a rectangle with dimensions 24 inches and 18 inches. The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the lengths of the other two sides:

\[
c^2 = a^2 + b^2
\]

where:
- \(c\) is the length of the diagonal,
- \(a\) is one side (24 inches),
- \(b\) is the other side (18 inches).

Now, we can plug in these values:

\[
c^2 = 24^2 + 18^2
\]
\[
c^2 = 576 + 324
\]
\[
c^2 = 900
\]

Now, we take the square root of both sides to find \(c\):

\[
c = \sqrt{900} = 30
\]

So, the diagonal length of the bottom of the box is **30 inches**.