SOLUTION: Please can you help me solve this. I tried but i have no idea if it is right. A cuboid box has dimensions 40cm x 30cm x 20cm. The box is to hold knitting needles. What is the s

Question 652002: Please can you help me solve this. I tried but i have no idea if it is right.
A cuboid box has dimensions 40cm x 30cm x 20cm. The box is to hold knitting needles. What is the size of the biggest knitting needle the box can hold ?
I tried a few things such as:

n = 44.7cm to 1 d.p.
Am I doing it right or not ?

Answer by kevwill(135) (Show Source): You can put this solution on YOUR website!
You're halfway to the correct answer. We'll take it in two parts.
If we assume the box is 40 cm long and 20 cm wide, you have answered the question "What is the longest knitting needle that can fit flat on the bottom of the box?" That is, you have found the length of the hypotenuse of the bottom of the box. Let's call it a, so we have
If we want to find the longest knitting needle that will fit in the box from, say, the bottom left front corner to the top right back corner, we start with the hypotenuse you found in the first step, and let that be one leg of another right triangle, with the height of the box (30 cm) being the second leg. Then the 3-dimenstional hypotenuse, c, is:

In general, for a 3-dimensional rectangular prism of dimension l*w*h, the longest diagonal, c, is:

In this case:

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