Question

Solve Similar Triangles (advanced) Solve for X.

Answer 1

Given:

$m\angle B=90^\circ, m\angle D=90^\circ, AB=x, BD=9, BC=1, DE=5$.

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,

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

$\dfrac{x}{x+9}=\dfrac{1}{5}$

On cross multiplication, we get

$5x=x+9$

$5x-x=9$

$4x=9$

$x=\dfrac{9}{4}$

$x=2.25$

Therefore, the value of x is 2.25 units.