Question

A photocopy of a polygon was reduced to 70% of its original size. Then, the copy was again reduced to 70% of its size.
a.is the second photocopy similar to the original?
b.what is the ratio of the corresponding sides of the second photocopy to the original?

Answer 1

Step-by-step explanation:

Step 1 of 4

a) Yes, since the photo copy, is same which is reduced by 80% it remains similar. Because the angles stay the same and the ratios responding sides are proportional.

The following is the figure:



Answer 2

a). Photocopy of a polygon reduced the size of the original polygon by

    70%.

    But the shape and angles of the the polygon remains unchanged.

    Therefore, all the photocopies will be similar to the original polygon.

b). Let the measure of a side of the original polygon measures 'x' unit.

    Size of the original polygon gets reduced by 70% in the photocopy.

    Then the measure of the side in the photocopy = x - (70% of x)

                                                                                    = $x-\frac{70x}{100}$

                                                                                    = $x-0.7x$

                                                                                    = $0.3x$ units

    Size of the second photocopy was reduced again by 70%.

  Therefore, measure of the side of the second polygon = $0.3x-(\frac{70}{100}\times 0.3x)$

                                                                                              = $0.3x-0.21x$

                                                                                              = $0.09x$ units

    Ratio of the corresponding sides of the second photocopy and the

    original = $\frac{0.09x}{x}$

                  = 0.09 : 1

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