The area of a base of a cuboid is 48 cm² and its height and length of the diagonal are 3 cm and 13 cm respectively. Calculate the length and width of the box?

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) m² and

length of diagonal = 

So accordingly

(a)(b)=48 ……………..(1) and

a²+b²=160-------------(2).

Now using formula. (a + b)² = a²+b²+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 = a² + b² - 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.