Question

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

Answer 1

`3`times 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 `3`times (`(12x) /(4x) = 3`)

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