Question

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

Answer 1

Answer:

I think it will be helpfull...

Answer 2

AnswEr :

• Side of Square = 64 m

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.3,2){\mathsf{\large{64 m}}}\put(7.7,1){\large{B}}\put(9,0.7){\matsf{\large{64 m}}}\put(10.6,1){\large{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){2}}\put(10.5,1){\line(0,3){2}}\put(8,3){\line(3,0){2.5}}\put(10.6,3){\large{D}}\end{picture}$

$\rule{150}{2}$

• Length of Rectangle = 70 m
• Breadth of Rectangle = ?

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.3,2){\mathsf{\large{? m}}}\put(7.7,1){\large{B}}\put(9.2,0.7){\matsf{\large{70 m}}}\put(11.1,1){\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,3){\large{D}}\end{picture}$

• According to the Question Now :

↠ Perimeter of Square Plot = Perimeter of Rectangluar Plot

↠ 4 × Side = 2 × (Length + Breadth)

• Dividing both term by 2

↠ 2 × Side = (Length + Breadth)

↠ 2 × 64m = (70m + Breadth)

↠ 128m = 70m + Breadth

↠ 128m – 70m = Breadth

↠ Breadth = 58 m

⠀

∴ Breadth of the Rectangluar Plot is 58 m.

$\rule{300}{2}$

• AREAS⠀OF⠀DIFFERENT⠀PLOT :

⇒ Rectangluar Plot = Length × Breadth

⇒ Rectangluar Plot = 70m × 58m

⇒ Rectangluar Plot = 4060 m²

$\rule{150}{2}$

⇒ Square Plot = ( Side )²

⇒ Square Plot = ( 64m )²

⇒ Square Plot = 4096 m²

⠀

∴ Hence, Area of Square Plot will be Greater and by (4096 – 4060)m² = 36 m².