Question

The area of the dining room at Thomas Jefferson’s home in Monticello is about 342 square feet. If the approximate length of the one side is a prime number less than 25, what are the approximate dimensions of the room?

• A. length = 172 feets and breadth = 2 feets
• B. length = 21 feets and breadth = 17 feets
• C. length = 19 feets and breadth = 18 feets
• D. length = 21 feets and breadth = 14 feets

Answer 1

The correct option is C length = 19 feets and breadth = 18 feets

Given, area of the dining room = 342 square feet.
We know that, area of rectangle = length x breadth
Implies, the length and breadth are the factors of 342
Prime factorisation of 342 = 2 x 3 x 3 x 19
Given that the approximate length of one side is a prime number less than 25.
The nearest prime number less than 25 and a factor of 342 is 19.
Therefore, the approximate length of the room = 19 feet
Hence, breadth =$\frac{area}{length}=\frac{342}{19}=18$ feet