A right triangle has sides 6, 8, and 10. A smaller triangle is drawn inside it with its vertices on the sides of the larger triangle, such that it is similar to the larger triangle. If the smaller triangle has a perimeter of 12, what is its area?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 6.
Perimeter of larger trianglke = 6 + 8 + 10 = 24
The smaller triangle is similar to it and has perimeter 12.
So the scale factor k from the big triangle to the small one is:
k =
Area of larger triangle = ½ × 6 × 8 = 24
Area scales by the square of the linear scale factor:
Asmall = k2 Alarge
⇒ Asmall = (½)2 × 24
⇒ Asmall = 24/4
⇒ Asmall = 6