Question

the area of a square is 144 cm square find the length of the side of a square

Answer 1

let the length of the square be X.

area of square= 144cm²

formula of area of square= (side)²

A/Q

(side)² = area

x² = 144

X=√144

X = 12 cm

Answer 2

$\textbf{\underline{Answer :-}}$

The side of the square is 12 cm

$\textbf{\underline{Explanation :-}}$

$\textsf{\underline{Given :- }}$

Area of the Square = 144 sq.cm

$\textsf{\underline{To find :-}}$

The measure of the side of the square.

$\textsf{\underline{Solution :-}}$

Area of the Square =

$\tt{\implies \: side \times side}$

Consider the side as x

$\tt{\implies \: x \times x = 144}$

$\tt{\implies \: {x}^{2} =144 }$

$\tt{\implies \: x = \sqrt{144} }$

The value of x is the Square root of 144

Square root :

$\begin{array}{r|l}2 & 144 \\\cline{1-2} 2 & 72 \\\cline{1-2} 2 & 36\\ \cline{1-2} 2 & 18 \\\cline{1-2} 3 & 9\\\cline{1-2}3&3\\\cline{1-2}& 1 \end{array}$

144 = 2 × 2 × 2 × 2 × 3 × 3

Make pairs of common Factors and take only one from them.

Square root = 2 × 2 × 3

Square root = 12

$\tt{\implies \: x = 12}$

Therefore the Side of the Square is 12 cm long.

$\textbf{\underline{Verification :-}}$

$\tt{\implies \: side \: \times side \: = 144}$

$\tt{\implies12 \times 12 = 144}$

$\tt{\implies144 = 144}$

$\therefore$LHS = RHS

$\therefore$The side of the square is 12 cm