Question

Two plots of land have the same perimeter.one is square of side 60m while the other is a rectangle whose breadth is 1.5 dam which plot has the greater area and by how much

Answer 1

Square perimeter = 4a = 4*60 = 240 m
Square area = 60*60 = 3600 m2

Rectangle perimeter = 2(l+b)
240 = 2(l+15)
120-15=l
l=105

Area = 105*15 = 1575m
Square has larger area

Answer 2

Given,

Length of each side of a square plot = 60 m

Length of the breath of a rectangular plot = 1.5 m

To find,

a) The plot that has a greater area

b) Difference between the area of the two plots

Solution,

We can simply solve this mathematical problem using the following process:

As per mensuration;

The perimeter of a square = 4 × (length of each side)

The area of a square = (length of each side)^2

The perimeter of a rectangle= 2 × (length + breadth)

The area of a rectangle = length × breadth

Now, according to the question;

The perimeter of the square plot = perimeter of the rectangular plot

=> 4 × (length of each side) = 2 × (length + breadth)

=> 2 × (60 m) = (length + 1.5 m)

=> length + 1.5 dam = 120 m

=> length + 15 m = 120 m

(As 1 dam = 1 decameter = 10 meters)

=> length = 105 m

Now, according to the question;

Area of the square plot

= (length of each side)^2

= (60 m)^2

= 3,600 m^2

And, area of the rectangular plot

= length × breadth

= 105 m × 15 m

= 1,575 m^2

Clearly, the square plot has a greater area than the rectangular plot by

= (area of the square plot) - (area of the rectangular plot)

= 3,600 m^2 - 1,575 m^2

= 2,025 m^2

Hence, the square plot has a greater area than the rectangular plot by 2,025 m^2.