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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

$3$ $3$ times or $200 %$ $200%$

Explanation:

Let the original square have a side of length = $x$ $x$

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

And its diagonal will be = $\sqrt{x^{2} + x^{2}}$ $sqrt(x^2+x^2$ (Pythagorous theorem)

or, diagonal = $\sqrt{2 x^{2}}$ $sqrt(2x^2$ = $x \sqrt{2}$ $xsqrt2$

Now, diagonal is increased by 3 times = $3 \times x \sqrt{2}$ $3xxxsqrt2$ ....(1)

Now, if you look at the length of the original diagonal, $x \sqrt{2}$ $xsqrt2$ , you can see that it is related to the original length $x$ $x$

Similarly, the new diagonal = $3 x \sqrt{2}$ $3xsqrt2$

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

Now, the new perimeter = $4 \times 3 x$ $4xx3x$ = $12 x$ $12x$ ----------(2)

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

Or, the increase in perimeter can be represented in percentage as = $\frac{12 x - 4 x}{4 x} \times 100$ $(12x-4x)/(4x)xx100$ = $200 %$ $200%$

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