Question

Find DE
13x-37
2x+13

Answer 1

DE = 27

Explanation:

From the picture attached,

Points D and E are the midpoints of the segments AC and BC and DE is the mid-segment joining these points.

By the mid-segment theorem,

A segment joining midpoints of the two sides of a triangle is parallel to the third side. length of mid-segment is half of the 3rd side in measure.

DC =
`(1)/(2)\text{AB}`

(2x + 13) =
`(1)/(2)(13x-37)`

2(2x + 13) = (13x - 37)

4x + 26 = 13x - 37

13x - 4x = 26 + 37

9x = 63

x = 7

DE = 2x + 13

= 2(7) + 13

= 14 + 13

= 27