A triangle has corners points A, B, and C. Side AB has a length of #5 #. The distance between the intersection of point A's angle bisector with side BC and point B is #3 #. If side AC has a length of #4 #, what is the length of side BC?

Answer 1

Length of side BC = 5.4

Let the point where the angle bisector intersects with side BC be D

#"using the "color(blue)"angle bisector theorem"#
#(AB)/(AC)=(BD)/(DC)#
#5 / 4 = 3 / (DC)#
#DC = (3*4) / 5 = 2.4#
#BC = BD+DC= 3+2.4 =5.4#
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Answer 2

Let D be the intersection point of the angle bisector of ∠A with side BC. According to the angle bisector theorem, BD/DC = AB/AC. Since AB = 5 and AC = 4, we have BD/DC = 5/4.

Let x be the length of BC. Then, BD + DC = x. Since BD = 5/9 * x and DC = 4/9 * x, we can write the equation:

5/9 * x + 4/9 * x = x

Solving for x:

9/9 * x = x x = 9

So, the length of side BC is 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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