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.

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

$\dfrac{x}{25}=\dfrac{(x+21)}{40}$

$40x=25(x+21)$

$40x=25x+525$

Isolating the x terms, we get

$40x-25x=525$

$15x=525$

$x=\dfrac{525}{15}$

$x=35$

Hence, the measure of AB is 35 m.