In triangle ABC two lines are drawn parallel to BC: DE with D on AB and E on AC, and FG with F on AB and G on AC. Triangle ADE has area nine forty-ninths of the area of triangle ABC, and triangle AFG has area twenty-five forty-ninths of the area of triangle ABC. Find AD : AF.

Question

Accepted Answer

3 : 5. Both small triangles are similar to ABC, so AD/AB = √9/49 = 3/7 and AF/AB = √25/49 = 5/7. Dividing one by the other, AD : AF = 3 : 5. The option 9 : 25 keeps the area ratio unrooted, while 3 : 7 and 5 : 7 are AD : AB and AF : AB, not the ratio asked for.

In triangle ABC two lines are drawn parallel to BC: DE with D on AB and E on AC, and FG with F on AB and G on AC. Triangle ADE has area nine forty-ninths of the area of triangle ABC, and triangle AFG has area twenty-five forty-ninths of the area of triangle ABC.
Find AD : AF.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Areas of Similar Triangles practice

In triangle ABC two lines are drawn parallel to BC: DE with D on AB and E on AC, and FG with F on AB and G on AC. Triangle ADE has area nine forty-ninths of the area of triangle ABC, and triangle AFG has area twenty-five forty-ninths of the area of triangle ABC.Find AD : AF.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Areas of Similar Triangles practice

In triangle ABC two lines are drawn parallel to BC: DE with D on AB and E on AC, and FG with F on AB and G on AC. Triangle ADE has area nine forty-ninths of the area of triangle ABC, and triangle AFG has area twenty-five forty-ninths of the area of triangle ABC.
Find AD : AF.