Question

9. A rectangle has an area equal to that of a square
of side 40 cm. If the breadth of the rectangle is 20
cm, find its length. Are the perimeters of the
rectangle and the square equal?​

Answer 1

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Answer 2

$\large{\underline{\underline{\mathfrak{\red{AnSwEr :}}}}}$

${\underline{\sf{\blue{Given :}}}}$

• Area of Square = Area of Rectangle

• Side of Square = 40 cm

• Breadth of Rectangle (B) = 20cm

$\rule{200}{1}$

${\underline{\sf{\green{Solution :}}}}$

$\star {\boxed{\sf{Area \: of \: Square \: = \: Side^2}}}$

And

${\bold{\star}} {\boxed{\sf{Area \: of \: Rectangle \: = \: Length \: \times \: breadth}}}$

A.T.Q,

$\implies {\sf{Side^2 \: = \: Length \: \times \: Breadth}}$

$\implies {\sf{(40)^2 \: = \: 20 \: \times \: Length}}$

$\implies {\sf{1600 \: = \: 20 \: \times \: Length}}$

$\implies {\sf{Length \: = \: \dfrac{\cancel{1600}}{\cancel{20}}}}$

$\implies {\sf{Length \: = \: 80 \: cm}}$

∴ Length is of 80 cm

$\rule{200}{1}$

Now,

$\star {\boxed{\sf{Perimeter \: of \: Square \: = \: 4 \: \times \: Side}}}$

$\implies {\sf{Perimeter \: = \: 4(40)}}$

$\implies {\sf{Perimeter \: = \: 160 \: cm}}$

∴ Perimeter of Square is 160 cm

$\rule{200}{1}$

$\star {\boxed{\sf{Perimeter \: of \: Rectangle \: = \: 2(Length \: + \: Breadth)}}}$

$\implies {\sf{Perimeter \: = \: 2(80 \: + \: 20)}}$

$\implies {\sf{Perimeter \: = \: 2(100)}}$

$\implies {\sf{Perimeter \: = \: 200 \: cm}}$

∴ Perimeter of Rectangle is 200 cm

So,

Perimeter Of Square ≠ Perimeter of Rectangle