Similar Figures Problem - Geometry

[omair_bba]

Hi, Below Q is not from any OG.


Q: In the figure, BD is parallel to EG, AD = 6, DG = 4, and triangle AEF has an area of 75. What is the area of triangle ABC ?

A) 27
B) 36
C) 45
D) 54
E) 63




Answer = A .

Please explain answer too !

Thankx...

[Javoni]

The triangles of ABC and AEF are similar because angle B and angle E are equal (BD paraller to EG and BC to EF). Also, angle A belongs to both triangles, no doubts, yep?! From here BC/EF = 6/10 = 3/5

There is one miraculous ratio for similar triangles that states following:

BC/EF = Square Root of (Area of ABC)/Square Root of (Area of AEF), This ratio is applicable to all similar triangles, I guess:

So we get: 3/5 = Sqr Root (X)/Sqr Root (75) >>> We will get 9*75 = 25*X, Hence X or the Area of triangle of ABC equals: 9*75/25 = 27
Answer: Area of triangle of ABC would be 27 - A

Please, correct me if I am wrong

Hi, Below Q is not from any OG.


Q: In the figure, BD is parallel to EG, AD = 6, DG = 4, and triangle AEF has an area of 75. What is the area of triangle ABC ?

A) 27
B) 36
C) 45
D) 54
E) 63




Answer = A .

Please explain answer too !

Thankx...

[huuquan]

The triangles of ABC and AEF are similar because angle B and angle E are equal (BD paraller to EG and BC to EF). Also, angle A belongs to both triangles, no doubts, yep?! From here BC/EF = 6/10 = 3/5

There is one miraculous ratio for similar triangles that states following:

BC/EF = Square Root of (Area of ABC)/Square Root of (Area of AEF), This ratio is applicable to all similar triangles, I guess:

So we get: 3/5 = Sqr Root (X)/Sqr Root (75) >>> We will get 9*75 = 25*X, Hence X or the Area of triangle of ABC equals: 9*75/25 = 27
Answer: Area of triangle of ABC would be 27 - A

Please, correct me if I am wrong

i think so. you're true

[ygdrasil24]

Step1: Consider TRi ABD, AEG : AD/DG = AB/BE = 3/5
Step2 : Consider Tri ABC & AEF : (AB/AE)^2=Area ABC/Area AEF ;
Solve 75*9/25 = 27.

Hence A

[vk_vinayak]

Hi, Below Q is not from any OG.


Q: In the figure, BD is parallel to EG, AD = 6, DG = 4, and triangle AEF has an area of 75. What is the area of triangle ABC ?

A) 27
B) 36
C) 45
D) 54
E) 63




Answer = A .

Please explain answer too !

Thankx...

RULE: For similar triangles, the ratio of areas = the ratio of squares of the corresponding sides.

From the figure we can see that AB=6 and BE=4. Hence AE = 10. Let the area of ABC be x.

According to the rule: (AE)^2 / (AB)^2 = 75 /x => 100/36 = 75/x

Solving for x, we get x=27. Hence Ans is A.

[Jim@StratusPrep]

Yup-

Good one to remember:

For similar triangles, the ratio of areas = the ratio of squares of the corresponding sides.

[omair_bba]

Thanks @Javoni & @vk_vinayak for ratio rule of similar triangles....
i.e RULE: For similar triangles, the ratio of areas = the ratio of squares of the corresponding sides.

I also solved below Q with the same rule...helped a lot !

Q: The figure shows a wedge-shaped holding tank that is partially filled with water. If the tank is 1/16 full, what is the depth of the water at the deepest part ?

A) 3
B) 2
C) 1.5
D) 1
E) 0.75



Answer = A .

Please confirm that this rule is also applicable here....