Question

I need help finding DE. I do not know what do to. Please help any tips will be appreciated:))

Answer 1

Given:

In triangle ABC,
`AB=11x-25,DE=4x+1`.

To find:

The measure of DE.

Solution:

From the given figure, it is clear that D is the midpoint of AC and E is the midpoint of BC. So, the line segment DE is the mid-segment of the triangle ABC.

According to the triangle mid-segment theorem, mid-segment of a triangle is equal to half of its base.

Using triangle mid-segment theorem, we get

`DE=(1)/(2)AB`

`(4x+1)=(1)/(2)(11x-25)`

`2(4x+1)=11x-25`

`8x+2=11x-25`

Isolate the variable terms.

`8x-11x=-2-25`

`-3x=-27`

`x=(-27)/(-3)`

`x=9`

The value of x is 9. So,

`DE=4x+1`

`DE=4(9)+1`

`DE=36+1`

`DE=36+1`

`DE=37`

Therefore, the length of DE is 37 units.