Question

If two cubes of length of each side 2√6 are placed side by side,then the length of the diagonal of the cuboid so produced is ?

Answer 1

Step-by-step explanation:

Given :-

Two cubes of length of each side 2√6 are placed side by side.

To find:-

Find the length of the diagonal of the cuboid so produced ?

Solution :-

Given that :

Length of the cube = 2√6 units

If two cubes are placed side by side then the resulting solid is a cuboid

Then

Length of the cuboid =2× side of the cube

=>2×2√6

=> 4√6 units

Breadth of the cuboid = side of the cube

= 2√6 units

Height of the cuboid = side of the cube

= 2√6 units

We have

l = 4√6 units

b= 2√6 units

h = 2√6 units

We know that

The length of the diagonal of a cuboid =√(l^2+b^2+h^2) units

On Substituting these values in the above formula

=> d = √[(4√6)^2+(2√6)^2+(2√6)^2] units

=> d =√[(16×6)+(4×6)+(4×6)] units

=> d =√(96+24+24) units

=> d =√144 units

=> d = √(12)^2 units

=>d = 12 units

Therefore, d=12 units

Answer:-

The length of the diagonal of the cuboid is 12 units

Used Concept:-

• If two cubes are joined by placing them side by side then the resulting solid is a cuboid .
• The length of the cuboid is twice the length of the edge of the cube and breadth and height are remain same.

Used formulae:-

• The length of the diagonal of a cuboid =√(l^2+b^2+h^2) units
• l = length
• b = breadth
• h = height