Question

A board 7 feet 9 inches long is divided into three equal parts. What is the length of each part?
(a) 2 feet 9 inches
(b) 2 feet 7 inches
(c) 2 feet 12 inches
(d) 2 feet 13 inches

Answer 1

Hint:To know the length of each part of a divided board we have to divide 7 feet 9 inches by 3. Convert 7 feet 9 inches to inches then divide by 3 then you will get an answer in inches. But the answer in options in the mixture of inches and feet then divide the inches by 12 to get the answer in terms of feet.

Complete step-by-step answer:
In the following figure, we have drawn the board ABCD where AD is the length of the board.

In the question above, it is given that the length of the board i.e. AD is equal to 7 feet 9 inches and this length is divided into 3 equal parts.
AD = 7 feet 9 inches
Now, we are converting feet into inches.
1 feet = 12 inches
∴ 7 feet = 12×7 inches = 84 inches
So, the length of the AD in inches is equal to 84 + 9 = 93 inches.
Now, the length of the board is divided into 3 equal parts do dividing AD by 3 we get,
$\dfrac{AD}{3}$
Substituting the value of AD as 93 inches in the above expression we get,
$\dfrac{93}{3}=31$
So, after division of length by 3 we get 31 inches. But the answer is in the mixture of feet and inches.
So, 31 inches can be written as 2 feet 7 inches.
Hence, the correct option is (b).

Note: You might be wondering how we have converted 31 inches to 2 feet 7 inches.
Divide 31 by 12, the quotient i.e. 2 will give you the number of feet and the remainder i.e.7 will give you the number of inches. This is how we get 31 inches = 2 feet 7 inches.