Question

BD = 21 m,
RC = 25 m.
DE = 40 m.
AB = ? m.

Find AB

Answer 1

Given:

Consider the given sides are,

`BD=21m`

`BC=25m`

`DE=40m`

`AB=xm`

To find:

The measure of AB.

Solution:

Let x be the measure of AB.

From the given figure it is clear that,

`\angle ADE \cong \angle ABC` (Right angles)

`\angle ADE \cong \angle ABC` (Corresponding angles)

Two corresponding angles are congruent. So, by AA property of similarity,

`\Delta ABC\sim \Delta ADE`

Corresponding sides of similar triangle are proportional.

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

`(x)/(25)=((x+21))/(40)`

`40x=25(x+21)`

`40x=25x+525`

Isolating x, we get

`40x-25x=525`

`15x=525`

`x=(525)/(15)`

`x=35`

Therefore, the measure of AB is 35 m.