Question

The length breadth and height of two boxes are 3,4,6 and 3,5,h but their diagonal are equal find h.

Answer 1

Considering the first box. The dimensions i.e. length, width and height are 3, 4 and 6. I am giving notation for root as R and square as S. While taking note of this problem replace R with root symbol and S with square symbol.

The length of base diagonal is R(3S+4S) = R(9+16) = R(25) = 5

Now calculating the major (Box i.e. in Cuboid shape) diagonal, the two sides (of right angled triangle) will be height (6) and base diagonal (5). It is R(5S+6S) = R(25+36) = R(61).

Going to second Boxthe diomensions i.e. lenght, breadth and height are 3,5 and h.

The length of base diagonal is R(3S+5S) = R(9+25) = R(34)

For calculating the Box (major) diagonal, the two sides (of right angled triangle) will be height h and base diagonal (R(34)). It is R(hS+R(34)S). But this is equal to R(61).

R(hS+R(34)S) = R(61).

Squaring on both sides hS+34=61.

h = R(61-34)

h=R27

h=3R3

So the height of second box is 3root3.