Question 11 of 16intermediate🔧 ApplyNumerical3 marks

Find the sidelength of a rhombus whose diagonals are of length 24 units and 70 units.

Correct Answer

Given: Diagonals of a rhombus = 24 units and 70 units.

Step 1: In a rhombus, diagonals bisect each other at right angles. Step 2: Half of diagonal 1 = 24/2 = 12 units Step 3: Half of diagonal 2 = 70/2 = 35 units Step 4: These half-diagonals form the legs of a right triangle with the rhombus side as hypotenuse. Step 5: Apply Baudhāyana's Theorem: side² = 12² + 35² = 144 + 1225 = 1369 Step 6: side = 1369\sqrt{1369} = 37 units

Answer: The sidelength of the rhombus is 37 units.

Exercise: Figure it Out (Section 4) | Q: 3 | (Page Page 21)
For More Understanding

Explanation

In a rhombus, the diagonals bisect each other at right angles. This means each half-diagonal forms a leg of a right triangle, with the side of the rhombus as the hypotenuse. The chapter's application of Baudhāyana's Theorem to this geometric situation allows us to find the side length from the diagonal lengths.

Solution Steps

  1. Step 1: In a rhombus, diagonals bisect each other at right angles.

  2. Step 2: Half of diagonal 1 = 24/2 = 12 units

  3. Step 3: Half of diagonal 2 = 70/2 = 35 units

  4. Step 4: These half-diagonals form the legs of a right triangle with the rhombus side as hypotenuse.

  5. Step 5: Apply Baudhāyana's Theorem: side² = 12² + 35² = 144 + 1225 = 1369

  6. Step 6: Solve: side = 1369\sqrt{1369} = 37 units

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