Question

A square of side 40 cm and a rectangle of length 50 cm has the same perimeter. Which has greater area? Please write the answer with steps.

Answer 1

Answer: The square has greater area

Step-by-step explanation:

P(square) = 40 x 4 = 160

Find width of rectangle:

2(50 + W) = 160 (P(square) = P(rectangle)
100 + 2W = 160
2W = 60
W = 30

Find area of square:

A = 40 x 40 = 1600cm^2

Find area of rectangle:

A = 50 x 30 = 1500cm^2

Therefore, the area of square is greater than rectangle.

Answer 2

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Step-by-step explanation:

Perimeter of Square:

P = 4(Length)

P = 4(40)

P = 160 cm

This means that the rectangle also has a perimeter of 160 cm

So, Finding the width of rectangle by Perimeter formula:

2L + 2W = Perimeter

2(50) + 2W = 160

100 + 2W = 160

Subtracting 100 to both sides

2W = 60

Dividing both sides by 2

W = 30

Now, Area of Square:

Area = Length * Length

Area = 40 * 40

Area = 1600 cm²

Area of Rectangle:

Area = Length * Width

Area = 50 * 30

Area = 1500 cm²

When we compare both of the area of the figure, we come to know that the area of square is greater.