Suppose A B C is triangle and D, E are points on the sides AB and… - Vidyadip

MCQ

Suppose $A B C$ is triangle and $D, E$ are points on the sides $AB$ and $AC$ respectively. If $AD : AB =3: 5$ and $AE : AC =2: 3$, then the ratio of the areas of the triangles $ABC$ and $ADE$ lies in the interval.

A
$(1,2]$
✓
$\left(2, \frac{5}{2}\right]$
C
$\left(\frac{5}{2}, 3\right]$
D
$\left(3, \frac{7}{2}\right]$

✓

Answer

Correct option: B.

$\left(2, \frac{5}{2}\right]$

b
(b)

$\frac{\operatorname{ar} \triangle ABC }{\operatorname{ar} \triangle ADE }=\frac{\frac{1}{2} \cdot AB \cdot AC \sin \theta}{\frac{1}{2} \cdot AD \cdot AE \sin \theta}$

$=\frac{ AB }{ AD } \times \frac{ AC }{ AE }$

$=\frac{5}{3} \times \frac{3}{2}=\frac{5}{2}$

correct option is $\frac{5}{2}$

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