Question

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

Answer 1

Given Data:

• Two plots of land have same perimeter

• One is square of side 64 m
• The other is a rectangle of length 70m.

To Find:

Which plot has the greater area and by how much?​

solution:

first we need to find both the perimeters,

perimeter of square =perimeter of rectangle

perimeter of square = 4a units

                                 = 4×64m

                                 =256 m

to find the breadth of rectangle,

perimeter of rectangle = 2( l+ b)

∴perimeter of square =perimeter of rectangle

256 m = 2( l + b )

256     =2(70 + b)

256     =140 +2b

256 -140=2b

116 m = 2b

b=116/2

b=58 m

now we can find area for both,

area of rectangle = l × b sq.units

                             =70 ×58

                             =4060 $m^2$

area of square=$a^2sq.units$

                        =64 ×64

                        =4096 $m^2$

comparing the area of square and rectangle

area of square > area of rectangle

∴The square plot has the greater area of 4096 $m^2$