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

$DE=\dfrac{1}{2}AB$

$(4x+1)=\dfrac{1}{2}(11x-25)$

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

$8x+2=11x-25$

Isolate the variable terms.

$8x-11x=-2-25$

$-3x=-27$

$x=\dfrac{-27}{-3}$

$x=9$

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.