Question

the perimeter of a square is equal to that of a rectangle of length17m an breadth 11m.find the area of the square​

Answer 1

Answer:

given,

length and breadth of a rectangle are 17m & 11m respectively.

perimeter of a rectangle is 2(l+b),

= 2(17+11) = 56 m,

given that the perimeter of rectangle is equal to perimeter of a square,

i.e, 4a = 56,

=> a = 14m,

therefore,

the area of a square is a^2,

= 14*14 = 196 sq-m

Answer 2

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

➪ Area of the square is 196m² ${{{{{\textsf{\textbf{ ☑ }}}}}}}$

${\blue{\underline{\underline{\purple{\textsf{\textbf{Step-by-step explanation: }}}}}}}$

❐ Step 1:

➙ It's told that both figure is having same perimeter.

So,

Perimeter of them is given by :

➙ Perimeter of rectangle = 2(l + b)

➙ Perimeter of a square = 4*side

❐ Step 2:

$\begin{gathered}\underline{\:\boldsymbol{According\:to\:the\:question\::}}\ \ \end{gathered}$

$\sf \: : \implies \: perimeter \: of \:the \: square = perimeter \: of \: the \: rectangle$

$\sf \: : \implies \: 4 \times side = 2(l + b)$

$\sf \: : \implies \: 4 \times side = 2(17 + 11)$

$\sf \: : \implies \: 4 \times side = 2(28)$

$\sf \: : \implies \: 4 \times side = 56$

$\sf \: : \implies \: side = \frac{56}{4}$

$\sf \: : \implies \: side = 14m$

Now,

We got each side of the square 14metres.

❐ Step 3:

Area of the square is given by :

➙ Area of a square = (each side)²

So,

• Taking (a) as the area of square.

➙ a = (side)²

➙ a = (14m)

➙ a = 196m² ans.

${{\underline{\underline{{\textsf{\textbf{Hence, area of the square is 196m² ☑ }}}}}}}$

❐ Note behind :

• As it is given that the perimeter of both figure is equal. Hence, from the given values we are getting the each side of the square.
• Applying the formula of ‘Area of square’ we get our final answer.