Matt drew the diagram shown below and described it as an equilateral triangle with a square inside it. Point D is the midpoint of segment AC.
The geometry teacher pointed out that the triangle cannot be equilateral since side AC is not equal to AB.

Which statement best explains why the measurements are incorrect?
Answers:
Segment AB is 12 + 5 + 12 = 29.

Segment AB is 12 + 12 + 12 = 36.

Segment AB ≈ 12 + 12.5 + 12 ≈ 36.5.
or
Segment AB ≈ 12 + 17.7 + 12 ≈ 41.7.

Question

Matt drew the diagram shown below and described it as an equilateral triangle with a square inside it. Point D is the midpoint of segment AC.
 The geometry teacher pointed out that the triangle cannot be equilateral since side AC is not equal to AB.
 
Which statement best explains why the measurements are incorrect?
Answers:		
Segment AB is 12 + 5 + 12 = 29.
		
Segment AB is 12 + 12 + 12 = 36.
		
Segment AB ≈ 12 + 12.5 + 12 ≈ 36.5.
		or
Segment AB ≈ 12 + 17.7 + 12 ≈ 41.7.

anonymous · Answer

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anonymous · Answer

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Notice that AB has two pieces that are 12 long and then a piece in the middle that we don't know yet?
Well, since that piece is part of a square, it is exactly as long as the other sides of the square.
Now, notice the right triangle with hypotenuse 13 and one leg 12. Use that triangle to solve for the third side, and that side is the same length as the piece of AB that we don't know.