Using the constructions you have now seen, how would you construct a square whose area is triple the area of a given square? Class 8

Using the constructions you have now seen, how would you construct a square whose area is triple the area of a given square? Class 8

Question 1.

Using the constructions you have now seen, how would you construct a square whose area is triple the area of a given square? Five times the area of a given square? (Baudhayana’s Sulba- Sutra, Verse 1.10) Class 8

Solution:

Let ABCD be a given square of side a.

Then, AC = a[latex]\sqrt{2}[/latex] (By Baudhayana theorem)

Now, we shall construct a right triangle PQR with it two sides (other than hypotenuse) as a and a[latex]\sqrt{2}[/latex] as shown below :

Now, we shall construct a square PRST with one side as PR as shown in the figure. Then, area of square PRST is triple the area of square ABCD.

Because PR² = a² + (a[latex]\sqrt{2}[/latex] )² = 3a².

For a square of five times the area of ABCD, we shall first construct a right triangle EFG with two sides (other than hypotenuse) as QR = a[latex]\sqrt{2}[/latex] and PR = a[latex]\sqrt{3}[/latex] as shown below :

Now, we shall draw a square EHIG with one side as EG. Then, area of this square EHIG is five times the area of square ABCD, because EG² = (a[latex]\sqrt{2}[/latex] )² = (a[latex]\sqrt{3}[/latex] )² = 2a² + 3a² = 5a².