A triangle has corners at points A, B, and C. Side AB has a length of #36 #. The distance between the intersection of point A's angle bisector with side BC and point B is #14 #. If side AC has a length of #36 #, what is the length of side BC?

Answer 1

#28#

Consider the diagram

For that we use the angle bisector theorem

#color(red)("AB")/color(lightgreen)("BD")=color(blue)("AC")/color(brown)("DC")#

#:.36/14=36/("DC")#

So,

#color(brown)("DC"=14#

Then,the length of #"BC"# will be #color(lightgreen)("BD")+color(brown)("DC")=14+14=28#

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Answer 2

To find the length of side BC, we can use the Angle Bisector Theorem. According to this theorem, in a triangle, an angle bisector divides the opposite side into segments that are proportional to the other two sides of the triangle.

Given that side AB has a length of 36 and side AC has a length of 36, and the distance between the intersection of point A's angle bisector with side BC and point B is 14, we can set up the following proportion:

[ \frac{BC}{AC} = \frac{BD}{AD} ]

Where:

  • BC is the length of side BC.
  • AC is the length of side AC.
  • BD is the distance between the intersection of point A's angle bisector with side BC and point B.
  • AD is the length of the remaining portion of side AC.

We know that AC = 36 and BD = 14.

To find AD, we subtract BD from AC: [ AD = AC - BD = 36 - 14 = 22 ]

Now we can solve for BC: [ \frac{BC}{36} = \frac{14}{22} ]

Cross-multiplying: [ 22 \cdot BC = 14 \cdot 36 ] [ 22 \cdot BC = 504 ]

Dividing both sides by 22: [ BC = \frac{504}{22} ] [ BC = 22.9 ]

So, the length of side BC is approximately 22.9.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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