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In the diagram below of triangle ABC, D is a midpoint of AB and E is a midpoint
of BC. If DE = 4x + 4, and AC = x + 36, what is the measure of DE?
В.
D
E
A
С

In the diagram below of triangle ABC D is a midpoint of AB and E is a midpoint of BC If DE 4x 4 and AC x 36 what is the measure of DE В D E A С class=

Respuesta :

Dead3ill

Answer:

DE = 20 units

Step-by-step explanation:

GIVEN :-

  • D & E are the mid-points of AB & BC respectively.
  • DE = 4x + 4
  • AC = x + 36

TO FIND :-

  • Measure of DE

FACTS TO KNOW BEFORE SOLVING :-

  • The midsegment of a triangle is a line constructed by connecting the midpoints of any two sides of the triangle.
  • The Triangle Midsegment Theorem tells us that a midsegment is one-half the length of the third side (the base), and it is also parallel to the base.

PROCEDURE :-

According to Triangle Midsegment Theorem ,

[tex]DE = \frac{AC}{2}[/tex]

[tex]=> 4x + 4 = \frac{x + 36}{2}[/tex]

Multiplying 2 on both the sides ,

[tex]=> 2(4x + 4) = x + 36[/tex]

[tex]=> 8x + 8 = x + 36[/tex]

[tex]=> 8x - x = 36 - 8[/tex]

[tex]=> 7x = 28[/tex]

[tex]=> x = \frac{28}{7} = 4[/tex]

∴ DE = 4×4 + 4 = 20 units

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