Question

the length of a rectangular is 132cm and it's perimeter is equal to the perimeter of a square with side 100cm find the area of rectangle​

Answer 1

${ \underbrace{ \mathfrak{ \gray{Given : }}}}$

• The length of the rectangle is 132cm.
• The perimeter of the rectangle is equal to the perimeter of the square which is having a side of 100cm.

${ \underbrace{ \mathfrak{ \gray{To \: find : }}}}$

↪ The area of the rectangle.

${ \underbrace{ \mathfrak{ \gray{solution : }}}}$

We know that,

${ \underline{ \boxed{ \textsf{ \textbf{Perimeter \: of \: a \: square = \: side(4) }}}}}$

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

$\longmapsto \: \sf{perimeter \: of \: the \: square \: = perimeter \: of \: rectangle} \: \gray{(given)}$

$\sf \longmapsto \: 100(4) = perimeter \: of \: \: rectangle \:$

$\sf \therefore \: perimeter \: of \: a \: rectangle \: = 400cm.$

After calculation we get :

Perimeter of the rectangle is = 400cm.

Now,

We know that,

${ \underline{ \boxed{ \textbf { \textsf{perimeter \: of \: a \: rectangle \: = 2(l + b)}}}}}$

Where,

Perimeter of the rectangle is 400cm.

b (length) is 132cm.

Substituting the given values as follows :

$\sf\longmapsto \: 400cm = 2(132 +b )$

$\sf\longmapsto 200 = 264 + 2b$

$\sf\longmapsto 2b = 400 - 264$

$\sf\longmapsto b = { \cancel{\frac{136}{2}}}$

$\bf\therefore b = 68cm.$

Now we are having,

l (length) = 132cm.

b (breadth) = 68cm.

${\underbrace{ \textbf { \textbf{Required \: answer : }}}} \\{ \underline{ \boxed { \textbf{ \textsf{Area \: of \: the \: rectangle \: =132 * 68 = 8,976 cm. ans.}}}}}$