[Sulba-Sutras] Give a method to convert a rectangle into an isosceles triangle by dissection. Class 8

[Sulba-Sutras] Give a method to convert a rectangle into an isosceles triangle by dissection. Class 8

Question 1.

[Sulba-Sutras] Give a method to convert a rectangle into an isosceles triangle by dissection. Class 8

Solution:

Let PQRS be a given rectangle.

Taking AB = 2 PQ and BC = QR construct a rectangle ABCD.

Mark mid-points M and N of AB and CD respectively.

Join MD and MC.

Then, MDC is the required isosceles triangle equal in area to rectangle PQRS.

Question 2.

Which has greater area—an equilateral triangle or a square of the same sidelength as the triangle? Which has greater area—two identical equilateral triangles together or a square of the same sidelength as the triangle? Give reasons. Class 8

Solution:

A square of the same sidelength is greater than in area than the equilateral triangle, because area of the square is a² and that of equilateral triangle is [latex]\frac{\sqrt{3} a^2}{2}[/latex] of sidelengths a.

Area of two identical equilateral triangles of sidelengths ‘a’ will be greater than that of a square, because 2 × [latex]\frac{\sqrt{3} a^2}{2}[/latex] > a².