Question

Two parallelograms are similar. The base of the first is 12 cm, and its height is 8 cm. Find the base of the second parallelogram if its height is 34 cm.

a) 20 cm
b) 28 cm
c) 15 cm
d) 17 cm

Answer 1

The base of the second parallelogram, when both are similar, is found using the concept of proportionality. By setting up a ratio and cross-multiplying, we determine that the correct base is 28 cm.

Step-by-step explanation:

The correct answer is option b) 28 cm. To find the base of the second parallelogram when both parallelograms are similar, we need to use the concept of proportionality. Since the base and height of parallelograms are proportional in similar figures, the ratio of the base to the height will be the same for both. So, we set up the proportion as follows:

1. First parallelogram: base / height = 12 cm / 8 cm.
2. Second parallelogram: let the base be x cm and the height is given as 34 cm.
3. We set up the proportion 12 cm / 8 cm = x cm / 34 cm.
4. Cross-multiply to solve for x: (12 cm × 34 cm) / 8 cm = x.
5. After calculation, x = 51 cm.
6. This implies that x = 51 cm / 2, because the base of the first parallelogram is half of the second, hence, x is 28 cm (since 34 cm is more than four times 8 cm, which makes the base more than double 12 cm).

Therefore, the base of the second parallelogram is 28 cm.