Question
The length of a rectangular field is $8m$ and breadth is $2m$. If a square field has the same perimeter as this rectangular field, find which field has the greater area.
✓
Answer
Given, length of a rectangular field $= 8m$
Breadth of a rectangular field $= 2m$
Now, perimeter of rectangle $= 2 \times $ (Length + Breadth)
$= 2 \times (8 + 2) = 2 \times 10$
$= 20m$
$\therefore$ Area of rectangle = Length $\times $ Breadth $= 8 \times 2 = 16m^2$
According to the question,
Perimeter of square = Perimeter of rectangle
$4 \times $ Side $= 20$
$\Rightarrow\frac{4\times\text{Side}}{4}=\frac{20}{4}$ [dividing both sides by $4$]
$\Rightarrow Side = 5m$
Now, area of square = Side $\times $ Side $= 5 \times 5 = 25m^2$
Hence, the area of square field is greater than the area of rectangular field.
Breadth of a rectangular field $= 2m$
Now, perimeter of rectangle $= 2 \times $ (Length + Breadth)
$= 2 \times (8 + 2) = 2 \times 10$
$= 20m$
$\therefore$ Area of rectangle = Length $\times $ Breadth $= 8 \times 2 = 16m^2$
According to the question,
Perimeter of square = Perimeter of rectangle
$4 \times $ Side $= 20$
$\Rightarrow\frac{4\times\text{Side}}{4}=\frac{20}{4}$ [dividing both sides by $4$]
$\Rightarrow Side = 5m$
Now, area of square = Side $\times $ Side $= 5 \times 5 = 25m^2$
Hence, the area of square field is greater than the area of rectangular field.
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