Question

Mr. Woo wants to ship a fishing rod that is 42 inches long to his son. He has a box with the dimensions shown.

a)Find the square of the length of the diagonal across the bottom of the box.

b. Find the length from a bottom corner to the opposite top corner to the nearest tenth. Will the fishing rod fit?​

Answer 1

A.
`s^2=1,700`

B. 42.4 inches. It will fit.

Explanation:

A.

Let s = the length of the diagonal across the bottom of the box.

`w^2+l^2\\\\10^2+40^2 = s^2\\\\100+1,600 = s^2\\\\1,700 =s^2\\\\`

Therefore,
`s^2=1,700`

B.

Let r = the length from a bottom corner to the opposite top corner.

`h^2+s^2\\\\10^2+1,700=r^2\\\\100+1,700=r^2\\\\1,800=r^2 \\\\42.4=r`

Therefore, the length of the longest tube that will fit in the box is 42.4 inches.

Since the fishing rod is only 42 inches long, which is less than 42.4 inches, by only 0.2 inches, it means it will still fit.