Multiple choice

The perimeters of two similar triangles ABC and PQR are 78 cm and 46.8 cm, respectively. If PQ = 11.7, then the length of AB is

  1. 19.5 cm

  2. 23.4 cm

  3. 24 cm

  4. 20 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For similar triangles, the ratio of perimeters equals the ratio of corresponding sides. Perimeter(ABC) / Perimeter(PQR) = AB / PQ. 78 / 46.8 = AB / 11.7. AB = (78 * 11.7) / 46.8 = 19.5.

AI explanation

For similar triangles, the ratio of their corresponding sides is equal to the ratio of their perimeters. The scale factor between triangles ABC and PQR is 78 divided by 46.8, which simplifies to 5 divided by 3. Using the proportion AB / PQ = 5 / 3 and substituting PQ = 11.7, we get AB = 11.7 multiplied by 5 divided by 3. This calculation results in AB equal to 19.5 cm.

Keep practicing — related questions