Question

BAC ~ DECx = ___ units​

Answer 1

Given:

$\Delta BAC\sim \Delta DEC$

To find:

The value of x.

Solution:

We have,

$\Delta BAC\sim \Delta DEC$

The corresponding parts of similar triangles are proportional.

$\dfrac{AB}{ED}=\dfrac{AC}{EC}$

On substituting the values, we get

$\dfrac{24}{56}=\dfrac{2x}{3x+5}$

$\dfrac{3}{7}=\dfrac{2x}{3x+5}$

$3(3x+5)=2x(7)$

$9x+15=14x$

Subtract $9x$ from both sides.

$15=14x-9x$

$15=5x$

$\dfrac{15}{5}=x$

$3=x$

Therefore, the value of x is 3 units.