what is the length of the interior diagonal of the box whose sides are 60cm, 80cm, and 100cm

Answer 1

We could simplify this by using sides of 3, 4 and 5, just a smaller scale version, by dividing all by 20. Get the answer to that problem, then multiply back by 20 to get the final answer.

The diagonal from a top left corner to a bottom right corner could be calculated first by finding the length of a diagonal on one of the box faces as one side of a right triangle, with the other side as the height of the box. Then the interior diagonal is the hypotenuse.

If the height is 3, then a box face diagonal is the square root of 4 squared plus 5 squared or (16+25)^1/2 = square root of 41. Square the square root of 41 add it to 3 squared = 41+9=50 Take the square root of 50

= 5(2)^1/2 = about 5(1.414)= about 7.07

Try it with a different face, 3x4 and height 5

diagonal on the 3x4 is square root of 9+16 = 5 square 5 add it to square of the height 5 to get 50. Now take the square root which is about 7.07

Try it with another box face 3x5 and height 4

diagonal on the 3x5 is square root of 9+25 or square root of 34. Square that to get 34, add 16 to get 50.

Square root is about 7.07, or slightly bigger.

But we need to multiply by 20 to get the final answer. It's about 141.4 cm or slightly more.