Question

Solve Similar Triangles (advanced) Solve for X.

Answer 1

Given:

$m\angle B=90^\circ, m\angle D=90^\circ, AB=6, BD=4, BC=2, DE=x$.

To find:

The value of x.

Solution:

In triangles ABC and ADE,

$\angle B\cong \angle D$              (Right angles)

$\angle A\cong \angle A$              (Common angles)

$\Delta ABC\sim \Delta ADE$              (AA property of similarity)

We know that the corresponding sides of similar triangles are proportional. So,

$\dfrac{AB}{AD}=\dfrac{BC}{DE}$

$\dfrac{6}{(6+4)}=\dfrac{2}{x}$

$\dfrac{6}{10}=\dfrac{2}{x}$

$\dfrac{3}{5}=\dfrac{2}{x}$

On cross multiplication, we get

$3\times x=5\times 2$

$3x=10$

$x=\dfrac{10}{3}$

Therefore, the value of x is $\dfrac{10}{3}$ units.