Question

in figure ,DE parallel BC and AD:DB=5:4 Find area triangle DFE÷ area triangle CFB

Answer 1

THE ANSWER IS IN THE ATTACHMENT!!!

It is 25 / 81 .

Answer 2

Answer:

The ratio of the areas of the given triangle is 25:81

Solution:

Note: Refer the attached image

Let us assume, AD=5x and DB=4x  

Now in $\Delta A B C, D E \| B C$,  

Hence, $\Delta A D E \sim \Delta A B C$

$\frac{A D}{A B}=\frac{D E}{B C}$

$\frac{5 X}{9 X}=\frac{D E}{B C}$

$\frac{D E}{B C}=\frac{5}{9}$ ….(i)  

Again in $\Delta D E F \text { and } \Delta B F C$,  

$\angle E D F=\angle F C B$…….. (//alternative angles)  

$\angle \mathrm{DFE}=\angle \mathrm{BFC}$ ………. (//Vertically opposite angle)  

Hence $\Delta D E F \sim \Delta B F C$,

$\frac{A R E A O F \Delta}{A R E A O F \Delta}=\left\{\frac{D E}{B C}\right\}^{2}=\left\{\frac{5}{9}\right\}^{2}=\left\{\frac{25}{81}\right\}=\left[\frac{D E}{B C}\right]^{2}=\left[\frac{5}{9}\right]^{2}=\frac{25}{81}$

The ratio of the area of given triangles is 25:81