If the diagonal length of a square is tripled, how much is the increase in the perimeter of that square?

Please help the answer is tripled

1 Answer
Feb 2, 2018

3times or 200%

Explanation:

Let the original square have a side of length = x

Then its perimeter will be = 4x-------------(1)

And its diagonal will be = sqrt(x^2+x^2 (Pythagorous theorem)

or, diagonal = sqrt(2x^2 = xsqrt2

Now, diagonal is increased by 3 times = 3xxxsqrt2....(1)

Now, if you look at the length of the original diagonal, xsqrt2, you can see that it is related to the original length x

Similarly, the new diagonal = 3xsqrt2

So, 3x is the new length of the side of square having increased diagonal.

Now, the new perimeter = 4xx3x = 12x----------(2)

You can see on comparing (1) and (2) that the new perimeter has increased by 3times ((12x) /(4x) = 3)

Or, the increase in perimeter can be represented in percentage as = (12x-4x)/(4x)xx100 = 200%