Question

If the area of a square is equal to the area of a rectangle with length and breadth respectively 54 m and 24 m, then the length of the square is m.

• A. 26
• B. 34
• C. 36
• D. 46

Answer 1

The correct option is C 36

Area of rectangle
Length $\times$ Breadth = $54\times 24$ = $1296m^2$

Given that the square has the same area as that of the rectangle.

So, area of square = 1296 m${}^2$
Thus, side of square = $\sqrt{1296}$ m

We can calculate the square root of 1296 by division method as follows:

$\begin{array}{cc}& 36\\ 3& \overline{12}\overline{96}\\ & 09\\ 66& 0396\\ & 0396\\ & 0\end{array}$

Alternatively, we can also find square root using prime factorization method.

$1296=2\times 2\times 2\times 2\times 3\times 3\times 3\times 3$

There are two pairs of '2' and two pairs of '3' hence the square root is $2\times 2\times 3\times 3=36$

Therefore, the length of the square is 36 m.