Question 10 of 16beginner🔧 ApplyNumerical2 marks

Find the diagonal of a square with sidelength 5 cm.

Correct Answer

Given: Square with side length a=5a = 5 cm.

Formula: The diagonal dd forms the hypotenuse of a right triangle. By Baudhāyana's Theorem: d2=a2+a2=2a2d^2 = a^2 + a^2 = 2a^2 So, d=a2d = a\sqrt{2}

Substitution: d2=2×52=2×25=50d^2 = 2 \times 5^2 = 2 \times 25 = 50

Calculation: d=50=25×2=52d = \sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2} d≈5×1.414≈7.07d \approx 5 \times 1.414 \approx 7.07 cm

Answer: The diagonal is 52≈7.075\sqrt{2} \approx 7.07 cm.

Exercise: Figure it Out (Section 4) | Q: 1 | (Page Page 20)
For More Understanding

Explanation

The chapter establishes that for a square with side 'a', the diagonal has length a2\sqrt{2}. This comes from the fact that the diagonal forms the hypotenuse of an isosceles right triangle with the two sides of the square as the equal sides. Using Baudhāyana's theorem: diagonal² = a² + a² = 2a², so diagonal = a2\sqrt{2}.

Solution Steps

  1. Step 1: For a square with side 'a', the diagonal 'd' forms a right triangle with the two sides.

  2. Step 2: Apply Baudhāyana's Theorem: d² = a² + a² = 2a²

  3. Step 3: Substitute a = 5: d² = 2×252 \times 25 = 50

  4. Step 4: Solve for d: d = 50\sqrt{50} = \sqrt{$$25 \times 2$$} = 52\sqrt{2}

  5. Step 5: Approximate: d ≈\approx 5×1.4145 \times 1.414 ≈\approx 7.07 cm

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