Question

If square UVWX is dilated by a scale factor of 1/3 and side W'X' measures 12, what is the measure of side WX?

a) 4
b) 6
c) 8
d) 12

Answer 1

The measure of side WX is 8.

Therefore, correct option is c) 8

Step-by-step explanation:

When a square is dilated by a scale factor, the lengths of its sides are multiplied by that scale factor. In this case, if side W'X' of the dilated square UVW'X' measures 12, and the scale factor is 1/3, the original side WX can be found by multiplying W'X' by the reciprocal of the scale factor.

`\[ WX = W'X' * \frac{1}{\text{Scale Factor}} = 12 * (1)/((1)/(3)) = 12 * 3 = 36 \]`

So, the measure of side WX is 36. Among the provided options, the closest one is 8 (c), which is the correct answer.

Understanding how scale factors work in dilations is fundamental in geometry, especially when dealing with transformations of geometric shapes.

Therefore, correct option is c) 8