Problem 3 · Convert an area ratio into a length ratio · 3 points
Made by AI and not reviewed by a real person.
A triangle sits inside a larger, similar triangle. The region between them has five-fourths the area of the inner triangle, and their perimeters add to 130 cm. What is the larger perimeter?
- 78 cm
- 90 cm
- 650/9 cm
- 52 cm
- 65 cm
Show a hint
- The region between the triangles is only part of the outer triangle. What is the area of the whole outer triangle compared with the inner one?
- For similar triangles, the area ratio is the square of the perimeter ratio.
Show the answer and solution
Answer: A — 78 cm
The outer triangle has 1 + 5/4 = 9/4 times the inner triangle’s area. Its perimeter is therefore 3/2 times the inner perimeter, so the two perimeters are in the ratio 3:2. The larger perimeter is (3/5) × 130 = 78 cm. The tempting 90 cm comes from incorrectly using the area ratio 9:4 as the perimeter ratio.