Question

two fields have the same perimeter .one is square of side 72 m and another is a rectangle of length 80m and breadth .which plot has a greater area and and by how much​

Answer 1

$\huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

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

Side of the square is 72 m.

Length of rectangle is 80m.

____________________________

$\Large{\underline{\bf{To \: Find \: :}}}$

Which have the greater area and by how much ?

____________________________

$\Large{\underline{\bf{Solution \: :}}}$

We know that,

$\large{\boxed{\red{\sf{Perimeter \: of \: square = 4 \times side}}}}$

Perimeter = 4(72)

⟹ Perimeter = 288 m

$\large{\boxed{\purple{\sf{Perimeter = 288 \: m}}}}$

$\rule{200}{2}$

Now,

$\large{\boxed{\green{\sf{Perimeter \: of \: Rectangle = 2(l + b)}}}}$

(Putting Values)

⟹ 288 = 2(80 + b)

⟹ 288/2 = 80 + b

⟹ 144 = 80 + b

⟹ 144 - 80 = b

⟹ 64 = b

$\large{\boxed{\orange{\sf{Breadth \: (b) = 64 \: m}}}}$

$\rule{200}{2}$

$\large{\boxed{\pink{\sf{Area \: of \: square = Side \times side}}}}$

⟹ Area = 72 * 72

⟹ Area = 5184 m²

$\large{\boxed{\blue{\sf{Area = 5184 \: m^2}}}}$

$\rule{200}{2}$

Now,

$\large{\boxed{\red{\sf{Area \: of \: rectangle = Length \times Breadth}}}}$

⟹ Area = 64 * 80

⟹ Area = 5120

$\large{\boxed{\purple{\sf{Area = 5120 \: m^2}}}}$

$\rule{200}{2}$

Greater area is of square.

⟹ 5184 - 5120 = 64 m²

So,

Area of square is greater than area of rectangle by 64 m².

$\rule{200}{2}$

#BAL

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