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

`(HE)/(GF)=(DE)/(DF)`

On substituting the values from the figure, we get

`(8)/(12)=(x)/(x+2)`

`(2)/(3)=(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.