# What is the breadth of the solid block?

The length, breadth and height of a rectangular solid block are in the ratio of 5:3:2 respectively. If the total surface area of the block is 992 sq. cm. What is the breadth of the solid block?

- 12 cm
- 10 cm
- 14 cm
- 16 cm

Answer: 12(2)^{1/2} cm

Explanation:-

The ratio of length,breadth and height of rectangular solid box = 5: 3: 2

Let be thelenght, breadth and height of rectangular solid box = 5X, 3X and 2X

Formula–

Total surface area of the bock = (lb + bh + hl)

According to the question,

(5X x 3X + 3X x 2X + 2X x 5X) = 992

15X^{2} + 6X^{2} + 10X^{2} = 992

31X^{2} = 992

X^{2} = 992/31

X^{2} = 32

X = 4(2)^{1/2}

then, breadth = 3X = 3 x 4(2)^{1/2}

= 12(2)^{1/2} cm

Hence, the breadth of the block is 12(2)^{1/2} cm