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,

`(AB)/(AD)=(BC)/(DE)`

`(x)/(x+9)=(1)/(5)`

On cross multiplication, we get

`5x=x+9`

`5x-x=9`

`4x=9`

`x=(9)/(4)`

`x=2.25`

Therefore, the value of x is 2.25 units.