[Sulba-Sutras] Give a method to obtain a rectangle of the same area as a given triangle. Class 8

[Sulba-Sutras] Give a method to obtain a rectangle of the same area as a given triangle. Class 8

Question 1.

[Sulba-Sutras] Give a method to obtain a rectangle of the same area as a given triangle. Class 8

Solution:

Construct a rectangle of length equal to the base of the triangle and breadth equal to double the corresponding height of the triangle.

Question 2.

[Sulba-Sutras] An isosceles triangle can be converted into a rectangle by dissection in a simpler way. Can you find out how to do it? Class 8

[Hint : Show that triangles ∆ADB and ∆ADC can be made into halves of a rectangle. Figure out how they should be assembled to get a rectangle. Use cut-outs if necessary.]

Solution:

∆ABC ≅ ∆ADC (By RHS)

Now, cut ∆ABD along AC into two halves. Now, place cut out of ∆ADC on ∆ABC such that C falls on A, A falls on C and D falls on opposite side of AB as shown on next page :

Then, rectangle ADBC is the required convertion.