Question 14 of 16beginner🔧 ApplyShort Answer2 marks

Give 5 examples of rectangles whose sidelengths and diagonals are all integers.

Correct Answer

Five examples of rectangles with integer sidelengths and integer diagonals:

(1) 3×43 \times 4 rectangle with diagonal 5 (2) 6×86 \times 8 rectangle with diagonal 10 (3) 5×125 \times 12 rectangle with diagonal 13 (4) 8×158 \times 15 rectangle with diagonal 17 (5) 9×129 \times 12 rectangle with diagonal 15

Note: Each rectangle's dimensions and diagonal form a Baudhāyana triple, satisfying a² + b² = c².

Exercise: Figure it Out (Section 4) | Q: 6 | (Page Page 21)
For More Understanding

Explanation

The chapter explains that a rectangle with sides a and b has a diagonal that forms the hypotenuse of a right triangle with legs a and b. For the diagonal to be an integer, (a, b, diagonal) must form a Baudhāyana triple. The chapter lists several such triples including (3, 4, 5), (5, 12, 13), (8, 15, 17), and scaled versions like (6, 8, 10) and (9, 12, 15). Each triple directly corresponds to a rectangle with integer sides and integer diagonal.

Solution Steps

  1. A rectangle with sides a and b has a diagonal that forms the hypotenuse of a right triangle with legs a and b.

  2. For the diagonal to be an integer, (a, b, diagonal) must form a Baudhāyana triple.

  3. Use known Baudhāyana triples: (3, 4, 5), (5, 12, 13), (8, 15, 17), and scaled versions like (6, 8, 10) and (9, 12, 15).

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