Assessment: Areas of Similar Triangles

Two similar triangles have a side ratio of 2:3. What is the ratio of their areas?

For similar triangles, does the perimeter scale the same way as the area?

Two similar triangles have corresponding sides 4 and 10. The smaller triangle has area 12. Find the larger triangle's area.

Two similar triangles have corresponding sides 7 and 21. The smaller triangle's perimeter is 15. Find the larger triangle's perimeter.

Two similar triangles have areas 27 and 48. A side of the smaller triangle is 6. Find the corresponding side of the larger triangle.

Two similar triangles have a perimeter ratio of 5:8. The larger triangle's area is 128. Find the smaller triangle's area.

A garden designer doubles every side length of a triangular flower bed. If the original needed 5 bags of mulch to cover it, how many bags will the new bed need?

A fencing contractor quotes a triangular yard scaled up by a factor of 3 in every linear dimension. How does the amount of fencing needed change?

Why does perimeter scale linearly with the scale factor k, while area scales with k²?

Two similar triangles have an area ratio of 49:4. The smaller triangle's longest side is 8. Find the larger triangle's longest side.