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,

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

`(6)/((6+4))=(2)/(x)`

`(6)/(10)=(2)/(x)`

`(3)/(5)=(2)/(x)`

On cross multiplication, we get

`3* x=5* 2`

`3x=10`

`x=(10)/(3)`

Therefore, the value of x is
`(10)/(3)` units.