A square and a rectangular field has the same perimeters.the dimension

1.	A square and a rectangular field has the same perimeters.the dimension of rectangular field are 120m *90m .find out which field has the greater area
Answer» Given :- Length of the rectangle = 120 m Breadth of the rectangle = 90 m Perimeter of square = Perimeter of rectangle To Find :- The field which has the greater area. Analysis :- First find the area of the rectangle using it's RESPECTIVE formula. Next find the side of the square field by FINDING the perimeter and dividing it by four. Then find the area accordingly. Solution :- We know that, l = Length a = Area p = Perimeter b = Breadth By the formula, $\underline{\boxed{\sf Area \ of \ the \ rectangle=Length \times Breadth}}$ Given that, Length (l) = 120 m Breadth (b) = 90 m Substituting their values, Area = 120 × 90 Area = 10800 m² By the formula, $\underline{\boxed{\sf Perimeter \ of \ rectangle=2(Length +Breadth) }}\\$ Substituting their values, = 2(120 + 90) = 2(210) = 420 m Given that, Perimeter of square = Perimeter of rectangle 420 m = 420 m According to the question, $\underline{\boxed{\sf Perimeter \ of \ a \ square=4 \times Side}}$ Substituting their values, 420 = 4 × s s = 420/4 s = 105 m Then, $\underline{\boxed{\sf Area \ of \ a \ square=Side \times Side}}$ Substituting their values, Area = 105 × 105 Area = 11025 m² Therefore, the area of the square is greater than that of rectangle.

A square and a rectangular field has the same perimeters.the dimension of rectangular field are 120m *90m .find out which field has the greater area

Answer»

Given :-

Length of the rectangle = 120 m

Breadth of the rectangle = 90 m

Perimeter of square = Perimeter of rectangle

To Find :-

The field which has the greater area.

Analysis :-

First find the area of the rectangle using it's RESPECTIVE formula.

Next find the side of the square field by FINDING the perimeter and dividing it by four.

Then find the area accordingly.

Solution :-

We know that,

l = Length
a = Area
p = Perimeter
b = Breadth

By the formula,

$\underline{\boxed{\sf Area \ of \ the \ rectangle=Length \times Breadth}}$

Given that,

Length (l) = 120 m

Breadth (b) = 90 m

Substituting their values,

Area = 120 × 90

Area = 10800 m²

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ rectangle=2(Length +Breadth) }}\\$

Substituting their values,

= 2(120 + 90)

= 2(210)

= 420 m

Given that,

Perimeter of square = Perimeter of rectangle

420 m = 420 m

According to the question,

$\underline{\boxed{\sf Perimeter \ of \ a \ square=4 \times Side}}$

Substituting their values,

420 = 4 × s

s = 420/4

s = 105 m

Then,

$\underline{\boxed{\sf Area \ of \ a \ square=Side \times Side}}$

Substituting their values,

Area = 105 × 105

Area = 11025 m²

Therefore, the area of the square is greater than that of rectangle.