Question

BD = 21 m.
BC= 25 m.
DE = 40 m.
AB = 7m.

Find AB

Answer 1

Given:

Let us consider the given sides are:

`BD=21m`

`BC=25m`

`DE=40m`

`AB=xm`

To find:

The length of side AB.

Solution:

Suppose the measure of AB be x.

From the given figure it is clear that,

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

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

In triangles ABC and ADE, two corresponding angles are congruent. So, by AA property of similarity,

`\Delta ABC\sim \Delta ADE`

We know that, corresponding sides of similar triangle are proportional.

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

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

`40x=25(x+21)`

`40x=25x+525`

Isolating the x terms, we get

`40x-25x=525`

`15x=525`

`x=(525)/(15)`

`x=35`

Hence, the measure of AB is 35 m.