In triangle ABC, D on AB and E on AC with DE parallel to BC. It is given that area(ADE) : area(ABC) = 4 : 9.
A student claims AD : DB = 2 : 1.
Determine the correct ratio AD : DB.

Question

In triangle ABC, D on AB and E on AC with DE parallel to BC. It is given that area(ADE) : area(ABC) = 4 : 9. A student claims AD : DB = 2 : 1. Determine the correct ratio AD : DB.

Accepted Answer

2:1. AD:AB = √4/9 = 2:3, so AD = 2 parts, AB = 3 parts, DB = AB - AD = 1 part. Hence AD:DB = 2:1. The student is correct.

In triangle ABC, D on AB and E on AC with DE parallel to BC. It is given that area(ADE) : area(ABC) = 4 : 9.
A student claims AD : DB = 2 : 1.
Determine the correct ratio AD : DB.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Areas of Similar Triangles practice

In triangle ABC, D on AB and E on AC with DE parallel to BC. It is given that area(ADE) : area(ABC) = 4 : 9.A student claims AD : DB = 2 : 1.Determine the correct ratio AD : DB.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Areas of Similar Triangles practice

In triangle ABC, D on AB and E on AC with DE parallel to BC. It is given that area(ADE) : area(ABC) = 4 : 9.
A student claims AD : DB = 2 : 1.
Determine the correct ratio AD : DB.