The perimeters of two similar triangles ΔRST and ΔABC are 26 cm and 39 cm, respectively. If AB = 24 cm, then RS is ___.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 16 cm.
The perimeters of two similar triangles, ΔRST and ΔABC, are 26 cm and 39 cm, respectively.
As the two triangles are similar, the ratio of the corresponding sides is the same as the ratio of their perimeter.
So, Perimeter of ΔRST/Perimeter of ΔABC = 26/39 = 2/3
Also, RS/AB = 2/3
⇒ RS/24 = 2/3
⇒ RS = 48/3 = 16 cm
Therefore, the length of RS is 16 cm.