Question

In a square, doubling every side increases the area by $ 27 $ sq. units. What is the length of the side of the newly formed square?
A. $ 3 $
B. $ 6 $
C. $ 9 $
D. $ 18 $

Answer 1

Hint: Here first of all we will assume the unknown side of the square using the variable and accordingly frame the mathematical expression using the reference value. Area of the square can be given as the product of two sides.

Complete step-by-step answer:
Let us assume that the side of the square be $ = x $ unit
The area of the square $ = {x^2} $ Square units ….. (A)
When the side of the square is double,
Therefore, new side of the square $ = 2x $ units
Therefore, new area $ = 4{x^2} $ square units
Also, given that the area increases by $ 27 $ sq. units
 $ 4{x^2} = {x^2} + 27 $
Move the term with the variable on the left hand side of the equation. When you move any term from one side to the opposite side then the sign of the term also changes. Positive term becomes negative and vice-versa.
 $ 4{x^2} - {x^2} = 27 $
Find the difference of the terms on the left hand side of the equation –
 $ 3{x^2} = 27 $
Term multiplicative on one side is moved to the opposite side then it goes to the denominator.
 $ {x^2} = \dfrac{{27}}{3} $
Common factors from the numerator and the denominator cancel each other.
 $ {x^2} = 9 $
Take square-root on both the sides of the equation –
 $ \sqrt {{x^2}} = \sqrt 9 $
Square and square-root cancel each other.
 $ x = 3 $
Hence, the length of the newly formed square is $ = 2x = 2(3) = 6 $ units
From the given multiple choices, option B is the correct answer.
So, the correct answer is “Option B”.

Note: Be good in square and square -root of the numbers. Always remember that the square and square root cancels each other. Square is the number multiplied with itself twice. Be careful while framing the mathematical expression from the given word statements and cross-check it.