Question

ADHE - ADGF below. Find the value of 'x'. X H н E 8 2. 12

Answer 1

Given:

$\Delta DHE\sim \Delta DGF$

To find:

The value of x.

Solution:

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

Since,$\Delta DHE\sim \Delta DGF$, therefore

$\dfrac{HE}{GF}=\dfrac{DE}{DF}$

On substituting the values from the figure, we get

$\dfrac{8}{12}=\dfrac{x}{x+2}$

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

On cross multiplication, we get

$2(x+2)=3x$

$2x+4=3x$

$4=3x-2x$

$4=x$

Therefore, the value of x is 4.