Question 8 of 14intermediate🔧 ApplyLong Answer3 marks

[Śulba-Sūtras] An isosceles triangle can be converted into a rectangle by dissection in a simpler way. Can you find out how to do it?

Correct Answer

Step 1: Draw the altitude from the apex to the base, which bisects the base.

Step 2: This divides the isosceles triangle into two congruent right triangles.

Step 3: Cut one right triangle and rotate it 180°.

Step 4: Join the two right triangles along their hypotenuses to form a rectangle.

The rectangle has length = half the base of the triangle, and width = height of the triangle.

Why it works: In an isosceles triangle, the altitude to the base creates two congruent right triangles that can be rearranged to form a rectangle.

Exercise: Figure it Out (Section 4) | Q: 7 | (Page Page 17)
For More Understanding

Explanation

The chapter provides a hint that triangles ΔADB and ΔADC can be made into halves of a rectangle. In an isosceles triangle, the altitude to the base creates two congruent right triangles that can be rearranged to form a rectangle.

Solution Steps

  1. Step 1: Take isosceles triangle ABC with AB = AC.

  2. Step 2: Draw altitude AD to base BC, which bisects BC.

  3. Step 3: This creates two congruent right triangles ΔADB and ΔADC.

  4. Step 4: Rotate one triangle and join with the other to form a rectangle.

  5. Step 5: Rectangle dimensions: length = BD = DC, width = AD.

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