The diagonal of a square is 60 cm. Calculate its peremeter

Analyze the question: We're given the diagonal of a square (60 cm) and asked for its perimeter.

Concept: The diagonal of a square splits it into two right-angled isosceles triangles. By Pythagoras, if the side is s, then:

d² = s² + s² = 2s², so d = s√2

Solution:

1. Diagonal: s√2 = 60
2. Side: s = 60/√2 = (60√2)/2 = 30√2 cm
3. Perimeter = 4s = 4 × 30√2 = 120√2 cm

Check: s = 30√2 ≈ 42.43 cm, and the perimeter ≈ 169.7 cm. Also, 120√2 ≈ 169.7, so this matches. The diagonal check: 42.43 × 1.414 ≈ 60 ✓.

120√2 cm**.

Tip: For any square, Perimeter = 4 × (d/√2) = 2√2 × d. Here, 2√2 × 60 = 120√2. Memorize that the side equals the diagonal divided by √2, and you can solve this type of question quickly.