Chapter 12, Problem 15CR

To determine

To Calculate: The length of BC

Answer to Problem 15CR

The length of BC is $64$

Explanation of Solution

Given information:

D and E are the mid-points of $\overline{AB}$ and $\overline{AC}$

DE = $4x$

  $BC=2x+48$

Formula used:

Here, we are using Angle Angle similarity rule.

Calculation:

  

Here, In $\Delta ADE$ and $\Delta ABC$

  $\angle ADE=\angle ABC$ (corresponding angles)

  $\angle A=\angle A$ (common)

So, $\Delta ADE\sim \Delta ABC$ (by Angle Angle similarity rule)

Hence, $\frac{AD}{AB}=\frac{DE}{BC}$

  $\frac{AD}{AD+DB}=\frac{4x}{2x+48}$

  $\because AD=DB$

So, $\frac{AD}{2AD}=\frac{4x}{2x+48}$

  $2x+48=8x$

  $x=8$

Hence, $BC=2x+48$

Putting the value of x

  → $2\times 8+48$

  → $64$

Conclusion: Hence, the length of BC is $64$