Shapes $A$ and $B$ are similar.
a) Calculate the scale factor from shape $A$ to shape B.
b) Find the value of $r$.
Give each answer as an integer or as a fraction in its simplest form.
Not drawn accurately
Answer
Now, we need to find the value of r. Since the shapes are similar, the ratio of the corresponding sides is the same. We have \(\frac{r}{6} = \frac{3}{2}\). To solve for r, we can cross-multiply and get \(2r = 18\). Then, we can divide both sides by 2 to get \(r = \boxed{9}\).
Step 1 ：First, we need to find the scale factor from shape A to shape B. The scale factor is the ratio of the corresponding sides of the two shapes. In this case, we have \(\frac{6}{4} = \frac{3}{2}\). So the scale factor from shape A to shape B is \(\boxed{\frac{3}{2}}\).
Step 2 ：Now, we need to find the value of r. Since the shapes are similar, the ratio of the corresponding sides is the same. We have \(\frac{r}{6} = \frac{3}{2}\). To solve for r, we can cross-multiply and get \(2r = 18\). Then, we can divide both sides by 2 to get \(r = \boxed{9}\).
