Question

11.The area of a square and a rectangle are equal. If the side of the square is40 cm and the breadth of the rectangle is 25 cm, find the length of the rectangle. A.lso, find the perimeter of the rectangle. ​

Answer 1

$\bf{ \red{ \underline{Given :}}}$

• Area of square = Area of rectangle
• Side of the square is 40 cm
• Breadth of the rectangle is 25 cm

$\bf{ \red{ \underline{Find :}}}$

• length of the rectangle ??
• perimeter of the rectangle ??

$☯︎ \bf{ \green{ \underline{We \: know \: that, }}}$

$\bf{⟹Area \: of \: square = a {}^{2} }$

$\bf{⟹ (40) {}^{2} = 1600cm {}^{2}}$

$\bf{⟹Area \: of \: rectangle = l \times b}$

$\bf{ ⟹l \times 25 = 25 \: Lcm {}^{2} }$

$➥ \bf{ \purple{ \underline{According \: to \: the \: question}}}$

$\bf{⟹ Area \: of \: square = Area \: of \: rectangle}$

$\bf{⟹1600 = 25 \:L}$

$\bf{⟹25 \: L = 1600}$

$\bf{⟹L = \cancel \frac{1600}{25} = \cancel\frac{320}{5} = 64 \: cm}$

∴ length of Given rectangle is of 64 cm

And, now we know length and breadth of rectangle...

Length = 64 cm

Breadth = 25 cm

$\bf{⟹Perimeter = 2(l + b)}$

$\bf{⟹2(64 + 25)}$

$\bf{⟹2 \times 89 = 178cm}$

$\bf{ \orange{Perimeter \: of \: rectangle \: is \: { \boxed{178 \: cm}}}}★$