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# The area of a base of a cuboid is 48 cm^{2} and its height and length of the diagonal are 3 cm and 13 cm respectively. Calculate the length and width of the box?

- 6 cm, 12 cm
- 2 cm , 4 cm
- 12 cm , 4 cm
- 4 cm, 6 cm

Hint:

### The formula for the diagonal of a cuboid is =

## The correct answer is: 12 cm , 4 cm

### Let a be the length and b be the width and c be height of rectangular solid whose area of the base will be (ab) m^{2} and

length of diagonal =

So accordingly

(a)(b)=48 ……………..(1) and

a^{2}+b^{2}=160-------------(2).

Now using formula. (a + b)^{2 }= a^{2}+b^{2}+2.ab

(a + b)^{2 }= 160 + 2 × 48

(a + b)^{2 }= 160 + 96 = 256

Taking square root of both sides

or. a + b = 16……………(3)

and. (a - b)^{2 }= a^{2 }+ b^{2 }- 2.ab

( a- b)^{2 }= 160 – 96 = 64

Taking square root of both sides

or. a - b = 8…………………(4). ,

By adding eqn. (3) and (4) we get,

2a = 24.

a = 24/2 = 12 m.

Putting a = 12 in eqn. (3)

12 + b = 16

b = 16 – 12

b = 4 m.

Thus , length =12 m , width = 4 m.

Therefore, the correct option is c)12cm , 4cm.

^{2}+b

^{2}=160-------------(2).

^{2 }= a

^{2}+b

^{2}+2.ab

^{2 }= 160 + 2 × 48

^{2 }= 160 + 96 = 256

^{2 }= a

^{2 }+ b

^{2 }- 2.ab

^{2 }= 160 – 96 = 64

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