Question

Polygon q is a scaled copy of polygon p. Given that one side in polygon p is 4 and its corresponding side in q is 3, and another side in polygon p is x, and its corresponding side in q is y, if the value of x is 6, what is the value of y?

a) 4
b) 3
c) 2
d) 9

Answer 1

To find the length of a correspondingly scaled side in polygon q (y), we multiply the original side length in polygon p (x) by the scale factor (0.75). In this case, multiplying 6 by 0.75 gives us 4.5, and the nearest integer answer choice is 4.

Step-by-step explanation:

The student asked about the relationship between corresponding sides in scaled copies of polygons. Since we have one pair of corresponding sides with lengths 4 in polygon p and 3 in polygon q, we find the scale factor between the two polygons by dividing 3 by 4, which gives us a scale factor of 0.75. This means that every dimension in polygon q is 0.75 times the length of the corresponding dimension in polygon p. Knowing the scale factor and another side of length x in polygon p is 6, we multiply 6 by the scale factor (6 x 0.75) to find the length of side y in polygon q, which equals 4.5. However, since 4.5 is not an option in the multiple choices provided, and assuming a typo in the question, the nearest integer answer would be (a) 4.