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

I need help finding DE. I do not know what do to. Please help any tips will be appreciated-example-1
User Crwth
by
7.2k points

1 Answer

3 votes

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.

User Raymond Zhang
by
8.1k points

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