Question

Two fields have same perimeter. One is a rectangle of length 70 m and another is a square of side 51 m. Which field has greater area and what is its value?

• A. Square field, $2601{\text{m}}^2$
• B. Rectangular field, $2548{\text{m}}^2$
• C. Both Square and Rectangular field have same area
• D. Rectangular field, $2240{\text{m}}^2$

Answer 1

The correct option is A Square field, $2601{\text{m}}^2$

Given,
Length of rectangle = 70 m, Side of square = 51 m

Perimeter of square = 4 x Length of the side
= $4\times 51$
= $204m$

It is given that the perimeter of square and perimeter of rectangle is equal.
Perimeter of rectangle is 204 m
$\because$Perimeter of Rectangle = 2 (Length + Breadth)
$\Rightarrow 204=2(70+\text{Breadth})\Rightarrow 102=(70+\text{Breadth})\Rightarrow \text{Breadth}=32m$

Area of rectangle = Length x Breadth
= 32 x 70
$=2240{\text{m}}^2$...(1)
Area of Square
= Length of side x Length of side
=51 x 51
$=2601{\text{m}}^2$...(2)

From (1) and (2)
Area of square is greater than area of rectangle.