Chapter 8.5, Problem 7PSA

Solution

To Calculate: Value of x.

Value of x is $7.5$

Given information: AB = $6$ , AD = $4$ , DC = $6$ is provided in the question which will help to find the solution.

Formula used: Here, we are using angle side angle similarity.

  

Calculation: Here, $\angle ABD=\angle DBC$ (given)

And, In $\Delta ABD$ and $\Delta DBC$

  $\angle ABD=\angle DBC$ (given)

BD = BD (common)

  $\angle BAD=\angle BCD$ (angle opposite to equal sides are equal)

Hence, $\Delta ABD\sim \Delta DBC$ (by angle side angle similarity)

So, $\frac{AB}{AD}=\frac{BC}{DC}$

➔ $\frac{6}{4}=\frac{x}{5}$

➔ $x=\frac{15}{2}=7.5$

Hence, value of x is $7.5$