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Gnesinka [82]
3 years ago
5

Points B, D, and F are midpoints of the sides of triangle ACE. EC = 38 and DF = 16. Find AC. The diagram is not to scale.

Mathematics
2 answers:
Fudgin [204]3 years ago
7 0
You are correct. DF is half as long as AC since DF is the parallel midsegment to AC

AC = 2*DF
AC = 2*16
AC = 32

The info about EC = 38 is extra info most likely put in there to throw you off, or as a distraction.
IgorC [24]3 years ago
3 0

Answer:  Yes, the answer 32 is correct.  

Explanation: Since, According to the mid point theorem, the line segment connecting the midpoints of the two sides of a triangle is parallel to the third side and is half of the third side of triangle.

Here, FD is the line segment connecting to the midpoints F and D and it is parallel and half of the third side AC.

Thus, FD=AC/2⇒ AC=2FD

But, according to the question, FD=16 so, AC=2×16=32

Thus, AC=32 unit will be the answer.

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The perimeter of a triangle is 32 feet. One side of the triangle is 3 times the second side. The third side is 12 feet longer
Ivenika [448]

We have a triangle whose perimeter is 32 feet. Some information regarding the sides of the triangle is given:

GiveN:

  • One side is 3 times the second side.
  • Third side is 12 feet longer than the second side.

As we can see that, two sides of the triangle are defined the second sides. It means First and third side can be expressed in the form of second side.

  • So let the second side be x

Then,

  • First side = 3x
  • And, third side = x + 12

We know that, perimeters is the sum of the lengths of all sides of the triangle, So it can be written as:

3x + x + x + 12 = 32

Solving it further,

5x + 12 = 32

Subtracting 12 from both sides,

5x + 12 - 12 = 32 - 12

5x = 20

Dividing 5 from both sides,

\frac{5x}{5}  =  \frac{20}{5}

x = 4

Then,

  • First side = 3x = 12 feet
  • Second side = 4 feet
  • Third side = x + 12 = 16 feet

And we are done with the answer !!

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