Question

In the given figure $\Delta ABC\sim \Delta ADE$. If AE : EC = 4 : 7. If x is the length of perpendicular from A to DE, find the length of the perpendicular from A to BC in terms of 'x'.

• A. $\frac{15}{4}x$
• B. $\frac{11}{4}x$
• C. $\frac{13}{4}x$
• D. $\frac{9}{4}x$

Answer 1

The correct option is B

$\frac{11}{4}x$

In $\Delta AFE\&\Delta AGC$

$\angle A=\angle A$ (common)

$\angle AFE=\angle AGC\left({90}^{\circ }\right)$

So, $\Delta AFE\sim \Delta AGC$ (By AA Similarity)

So, $\frac{AC}{AE}=\frac{AG}{AF}$ ---- (1)

We know that, $\frac{AE}{EC}=\frac{4}{7}$ (Given)

Adding 1 both side we get,

$\frac{EC}{AE}+1=\frac{7}{4}+1\frac{EC+AE}{AE}=\frac{11}{4}$
$\frac{AC}{AE}=\frac{11}{4}$ ----------- (2)

From (1) & (2) we get,

$\frac{AG}{AF}=\frac{11}{4}\frac{AG}{x}=\frac{11}{4}\Rightarrow AG=\frac{11}{4}x$