Question

BAC ~ DEC

x = ___ 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.

`(AB)/(ED)=(AC)/(EC)`

On substituting the values, we get

`(24)/(56)=(2x)/(3x+5)`

`(3)/(7)=(2x)/(3x+5)`

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

`9x+15=14x`

Subtract
`9x` from both sides.

`15=14x-9x`

`15=5x`

`(15)/(5)=x`

`3=x`

Therefore, the value of x is 3 units.