abm1995
An angle bisector of a triangle divides the opposite side of the triangle into segments 6 cm and 5 cm long. A second side of the triangle is 6.9 cm long. Find the longest and shortest possible lengths of the third side of the triangle. Round answers to the nearest tenth of a centimeter.
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ash2326
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Do you have a figure?
abm1995
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there's no figure. /: sorry.
ash2326
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No worries, that's why it has asked for two answers. Let ABC be the triangle and AD be the angle bisector. Let BD=6 and DC=5
|dw:1359393342358:dw|
Do you understand the figure?
abm1995
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yes!
ash2326
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@abm1995 ??
abm1995
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do you want the choices?
abm1995
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a. 41.4 cm, 8.3 cm
b. 30 cm, 5.8 cm
c. 41.4 cm, 4.3 cm
d. 8.3 cm, 5.8 cm
abm1995
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does anyone understand this?
ash2326
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Now we can have either AB or AC as 6.9 cm, we don't know that. It's the second side.
Do you know Angle Bisector theorem?
abm1995
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no i don't./: i'm dumb.
abm1995
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do you know the answer? then when i figure it out you will say if i'm right or not?
ash2326
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Yeah, I'll do let me explain you angle bisector theorem
abm1995
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ok.
ash2326
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Angle bisector divides the side opposite to the angle in the same ratio as that of the other two sides of the triangle, for example here|dw:1359394184684:dw|
\[\frac{BD}{DC}=\frac {AB}{AC}\]
abm1995
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oh ok.
abm1995
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wouldn't the answer be B then?
ash2326
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here we have BD=6 DC=5
Now assume AB as 6.9, find AC ???
abm1995
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so b?
ash2326
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No not yet. We have to find one more thing, assume AC=6.9 and find AB
abm1995
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oh it'd be c then or a.
ash2326
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What did you get for AB?
abm1995
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8.3?
ash2326
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Yes, we don't know which is the second side AB or AC. So we can get either 8.3 or 5.8
abm1995
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so , d?
ash2326
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yes, did you understand?
abm1995
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yes! your a lot of help!
ash2326
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No Problem :)
abm1995
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i need help with a little more../: i'm behind in school. could you help me?
abm1995
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What is the value of x?
abm1995
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a. 5
b. 2.5
c. 7.5
d. 10
ash2326
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The two lines indicated with arrow are parallel, so the two triangles are similar
abm1995
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yes. i know.
ash2326
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\[\frac{x}{x+x+5}=\frac {x-2}{x-2+x+1}\]
Now solve for x
abm1995
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wouldn't it be 5 though?
ash2326
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yes, just plugin the value and check
abm1995
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ok, so my answer would be a 5?
ash2326
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check it, you should ascertain it yourself
abm1995
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i don't think it's 5.
ash2326
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What did you get when you plugged in x=5 ?
abm1995
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idk. i'm just trying to get this done. i'm so behind.
ash2326
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Relax and do this
\[\frac{x}{x+x+5}=\frac {x-2}{x-2+x+1}\]
\[\frac {x}{2x+5}=\frac{x-2}{2x-1}\]
Put x=5 and check
abm1995
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i got 1/3
ash2326
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Both sides?
abm1995
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yes. do you know the answer?
ash2326
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So 5 is the correct answer
abm1995
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do you know that it is?
ash2326
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yes, that's why we got the same thing on both sides. Check other options also, you'll see that the left side won't be equal to the right side
abm1995
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What similarity statement can you write relating the three triangles in the diagram below?
abm1995
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