Question

A student is given the rectangle and square. The student states that the two figures have the same perimeter. Is the student perfect? Explain your reasoning.

Answer 1

The student is correct. Due to the meaning of perimeter which is all sides added up to make a number total, it is possible for a square and a rectangle to have the same perimeter if the numbers add up.

Answer 2

Perimeter of rectangle = 2×[Length +Breadth]

Perimeter of Square=4 × Side

If both Rectangle and Square has Same Perimeter

→4 ×Side=2×[Length +Breadth]

Dividing both sides by 2

→2 ×Side=Length +Breadth

So, if sum of length and breadth of rectangle is equal to side of square multiplied by 2,then perimeter of rectangle and square will be equal.

Suppose, Length=4 units

Breadth =6 units

Then,2×Side of Square=(4+6)

Then , Side of Square=5 units

⇒So,there are infinite dimensions of Square and rectangle possible such that both have same perimeter.