Question

park.
10. Two plots of land have the same perimeter. One is a square of side 64 m and the other is a
rectangle of length 70 m. Find the breadth of the rectangular plot. Which plot has the
greater area and by how much?​

Answer 1

G I V E N :

• Two plots of land have the same perimeter. One is a square of side 64 m and the other is a rectangle of length 70 m.

T O F I N D :

• The Breadth of the rectangular plot = ?
• Which plot has the greater area and by how much.

S O L U T I O N :

★ Finding Perimeter of rectangle :

Let the Breadth of rectangle be x.

→ Perimeter of rectangle = 2(70 + x)

→ Perimeter of rectangle = 140 + 2x m

★ Finding Perimeter of rectangle :

➝ Perimeter of square = 4 × Side

➝ Perimeter of square = 4 × 64

➝ Perimeter of square = 256 m

In the question it is given that, two plots of land have the same perimeter :]

⛬ Perimeter of square = Perimeter of rectangle

⟶ 256 = 140 + 2x

⟶ 256 - 140 = 2x

⟶ 116 = 2x

⟶ x = 116 ÷ 2

⟶ x = 58 m

Hence, breadth of rectangle is 58 m.

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━

★ Finding Perimeter of rectangle :

➺ Area of rectangle = Length × Breadth

➺ Area of rectangle = 70 × 58

➺ Area of rectangle = 4060 m²

★ Finding Perimeter of square :

➻ Area of square = (Side)²

➻ Area of square = (64)²

➻ Area of square = 4096 m²

★ Finding which plot has the greater area and by how much :

⋙ Area of square - Area of rectangle

⋙ 4096 - 4060

⋙ 36 m²

⛬ The area of square is greater than area of rectangle by 36 m².

═════════════════════════

Answer 2

Given :

• Two plots of land have the same perimeter.
• One is a square of side 64 m and the other is a rectangle of length 70 m

To Find :

• Breadth of the rectangular plot
• Which plot has greater area and by how much

Solution :

• Let the breadth of rectangle be x

• According to the question :

• Perimeter of square plot

$\leadsto \bf Perimeter\:of\:square\:=\:4\: \times side$

$\leadsto \sf Perimeter\:of\:square\:=\:4\: \times 64$

$\leadsto {\boxed{\sf{\red{Perimeter\:of\:square\:=\:256\:m}}}}$

• Perimeter of rectangular plot

$\leadsto \sf Perimeter\:of\:rectangle\:=\:2( l\:+\:b)$

$\leadsto \sf Perimeter\:of\:rectangle\:=\: 2( 70\:+\:x)$

$\leadsto {\boxed{\sf{\red{Perimeter\:of\:rectangle\:=\: 140\:+\:2x}}}}$

• Now , equate both the perimeters since they are equal

$\bigstar \: \sf Perimeter\:of\:square\:=\:Perimeter\:of\:rectangle$

$\leadsto \sf 256\:=\: 140\:+\:2x$

$\leadsto \sf 2x\:=\: 256\:-\:140$

$\leadsto \sf 2x\:=\: 116$

$\leadsto \sf x\:=\: \dfrac{116}{2}$

$\star \: {\underline{\sf{\red{x\:=\:58}}}}$

• Now , finding area of square and rectangular plot :

• Area of square plot :

$\leadsto \sf Area\:of\:sqaure\:=\:{(Side)}^{2}$

$\leadsto \sf Area\:of\:sqaure\:=\:{(64)}^{2}$

$\leadsto {\boxed{\sf{\red{Area\:of\:sqaure\:=\:4096\:{m}^{2}}}}}$

• Area of rectangular plot :

$\leadsto \sf Area\:of\:rectangle\:=\: length\: \times breadth$

$\leadsto \sf Area\:of\:rectangle\:=\: 70\: \times 58$

$\leadsto {\boxed{\sf{\red{Area\:of\:rectangle\:=\:4060\:{m}^{2}}}}}$

• Area of square plot is more than that of rectangular plot

• By how much ?

$\bigstar \: \sf Area\:of\:square\:-\:Area\:of\:rectangle$

$\leadsto \sf 4096\:-\:4060$

$\leadsto {\underline{\sf{\red{36\:{m}^{2}}}}}$

_____________________