Question

Which has greater perimeter: a square plot of side 75cm or a rectangular plot with sides
100 m and 65m and by how much?​

Answer 1

Given:

• Side of the square plot = 75 cm

• Dimensions of the rectangular plot = 100 m & 65 m.

To calculate:

• Which has greater perimeter?

Calculation:

As per the given question, we'll first find the perimeter of the both plots then we'll compare both in order to find which one of both has greater perimeter.

But before calculating we'll first convert the given physical quantities in same units. Let us convert the dimensions of both plot in cm!!

Conversion:

• Side of the square plot = 75 cm [Already in cm]

• Dimensions of the rectangular plot = 100 m & 65 m.

→ Breadth = 100 m

→ Breadth = ( 100 × 100 ) cm

→ Breadth = 10000 cm

→ Length = 65 m

→ Length = ( 65 × 100 ) cm

→ Length = 6500 cm

Calculating perimeter of square plot :

→ Perimeter of square plot = 4 × side

→ Perimeter of square plot = ( 4 × 75 ) cm

→ Perimeter of square plot = 300 cm

Calculating perimeter of rectangular plot :

→ Perimeter of the rectangular plot = 2 ( l + b )

→ Perimeter of the rectangular plot = 2 ( 10000 + 6500 ) cm

→ Perimeter of the rectangular plot = 33000 cm

Clearly,

Perimeter of rectangular plot > Perimeter of square plot.

Hence, rectangular plot has greater perimeter.

How much?

Let us subtract the perimeter of square from the perimeter of rectangular plot in order to find by how much the perimeter of rectangular plot is greater than the perimeter of the square plot.

→ ( 33000 – 300 ) cm

→ 32700 cm

Hence, the perimeter of rectangular plot is 32700 more greater than the square plot.

Answer 2

For the square shaped plot:-

Side = $75 \ cm$

Perimeter of square = $4 · s$

∴ Perimeter = $4(75) \ cm$

⇒ Perimeter = $300 \ cm$

For the rectangular plot:-

Dimensions = $100 \ m \times 64 \ m$

Perimeter of rectangle = $2(l + b)$

∴ Perimeter = $2(100 + 65) \ m$

⇒ Perimeter = $330 \ m$

∵ 1 m = 100 cm,

⇒ Perimeter = $330 · 100 \ cm = 33000 \ cm$.

Thus, perimeter of rectangular plot is greater than the square plot by 32700 cm.