Question : $D$ and $E$ are points of the sides $AB$ and $AC$, respectively of $ riangle ABC$ such that $DE$ is parallel to $BC$ and $AD:DB=7: 9$. If $CD$ and $BE$ intersect each other at $F$, then find the ratio of areas of $ riangle DEF$ and $ riangle CBF$.
Option 1: 49 : 144
Option 2: 49 : 81
Option 3: 49 : 256
Option 4: 256 : 49

Question

Question : $D$ and $E$ are points of the sides $AB$ and $AC$, respectively of $ riangle ABC$ such that $DE$ is parallel to $BC$ and $AD:DB=7: 9$. If $CD$ and $BE$ intersect each other at $F$, then find the ratio of areas of $ riangle DEF$ and $ riangle CBF$.

Option 1: 49 : 144

Option 2: 49 : 81

Option 3: 49 : 256

Option 4: 256 : 49

Team Careers360 · Accepted Answer

Correct Answer: 49 : 256

Solution :
Since $\angle A$ is common and $DE||BC$, $ riangle ADE\sim riangle ABC$
And given: $AD:DB=7:9$
⇒ $AD:(AD+DB) = 7:(7+9)$
$ herefore AD:(AB)= 7:16$
Since $ riangle ADE\sim riangle ABC$,
$AD:AB = DE:BC = AE:AC = 7:16$
Since $DE||BC$,
$\angle FDE= \angle FCB$ (alternate interior angles)
$\angle FED = \angle FBC$ (alternate interior angles)
And $\angle DFE = \angle CFB$ (vertically opposite angles)
So, $ riangle DEF\sim riangle CBF$ by AAA criteria
Now, the area of similar triangles is proportional to squares of sides of triangles.
So, Area ($ riangle DEF$) : Area ($ riangle CBF$) = $DE^2:BC^2$
⇒ Area($ riangle DEF$) : Area ($ riangle CBF$) = $7^2 : 16^2$
$ herefore$ Area ($ riangle DEF$) : Area($ riangle CBF$) = 49 : 256
Hence, the correct answer is 49 : 256.

Exams

Colleges

Predictors

Resources

Quick links

Exams

Colleges & Courses

Predictors

Resources

Exams

Colleges

Predictors & E-Books

Resources

Engineering Preparation

Medical Preparation

Law Preparation

MBA Preparation

Exams

Colleges

Resources

Exams

Colleges

Predictors & Articles

Resources

Exams

Colleges

Predictors

Resources

Exams

Colleges

Upcoming Events

Resources

Exams

Colleges

Resources

Quick Links

Top Streams

Specializations

Resources

Top Providers

Exams

Colleges

Resources

Diploma Colleges

Exams

Colleges

Resources

Exams

Resources

Top Courses & Careers

Colleges

Exams

Upcoming Events

Resources

Other Exams

Exams

Colleges

Top Countries

Resources

Exams

Top Schools

Products & Resources

NCERT Study Material

Question : D and E are points of the sides AB and AC, respectively of △ABC such that DE is parallel to BC and AD:DB=7:9. If CD and BE intersect each other at F, then find the ratio of areas of △DEF and △CBF.Option 1: 49 : 144Option 2: 49 : 81Option 3: 49 : 256Option 4: 256 : 49

Related Questions

Know More about

Upcoming Exams

Trending Articles around SSC CGL

Download the Careers360 App on your Android phone

Sign In/Sign Up