Question

The sides of a square are 4 centimetres long. The midpoints of the sides are joined to form another square as shown below

What is the perimeter of the smaller square?

Answer 1

Given: ABCD and PQRS are squares.

P, Q, R and S are the mid points of the sides AD, AB, BC and CD of the square ABCD.

AB = BC = CD = DA = 4 cm

P and Q are the midpoints of AD and AB respectively.

Now, in ΔAPQ, ∠PAQ = 90° (Angle of a square)

So, by using Pythagoras theorem, we have:

Now, PQRS formed inside the square ABCD is also a square.

∴ PQ = QR = RS = SP ≈ 2.83 cm

We know that perimeter of a square is equal to four times the length of its side.

∴ Perimeter of square PQRS ≈ 4 × 2.83 cm = 11.32 cm

Thus, the perimeter of square PQRS is approximately equal to 11.32 cm.