anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ash2326
  • ash2326
Do you have a figure?
anonymous
  • anonymous
there's no figure. /: sorry.
ash2326
  • ash2326
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?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
yes!
ash2326
  • ash2326
@abm1995 ??
anonymous
  • anonymous
do you want the choices?
anonymous
  • anonymous
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
anonymous
  • anonymous
does anyone understand this?
ash2326
  • ash2326
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?
anonymous
  • anonymous
no i don't./: i'm dumb.
anonymous
  • anonymous
do you know the answer? then when i figure it out you will say if i'm right or not?
ash2326
  • ash2326
Yeah, I'll do let me explain you angle bisector theorem
anonymous
  • anonymous
ok.
ash2326
  • ash2326
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| \[\frac{BD}{DC}=\frac {AB}{AC}\]
anonymous
  • anonymous
oh ok.
anonymous
  • anonymous
wouldn't the answer be B then?
ash2326
  • ash2326
here we have BD=6 DC=5 Now assume AB as 6.9, find AC ???
anonymous
  • anonymous
so b?
ash2326
  • ash2326
No not yet. We have to find one more thing, assume AC=6.9 and find AB
anonymous
  • anonymous
oh it'd be c then or a.
ash2326
  • ash2326
What did you get for AB?
anonymous
  • anonymous
8.3?
ash2326
  • ash2326
Yes, we don't know which is the second side AB or AC. So we can get either 8.3 or 5.8
anonymous
  • anonymous
so , d?
ash2326
  • ash2326
yes, did you understand?
anonymous
  • anonymous
yes! your a lot of help!
ash2326
  • ash2326
No Problem :)
anonymous
  • anonymous
i need help with a little more../: i'm behind in school. could you help me?
anonymous
  • anonymous
What is the value of x?
1 Attachment
anonymous
  • anonymous
a. 5 b. 2.5 c. 7.5 d. 10
ash2326
  • ash2326
The two lines indicated with arrow are parallel, so the two triangles are similar
anonymous
  • anonymous
yes. i know.
ash2326
  • ash2326
\[\frac{x}{x+x+5}=\frac {x-2}{x-2+x+1}\] Now solve for x
anonymous
  • anonymous
wouldn't it be 5 though?
ash2326
  • ash2326
yes, just plugin the value and check
anonymous
  • anonymous
ok, so my answer would be a 5?
ash2326
  • ash2326
check it, you should ascertain it yourself
anonymous
  • anonymous
i don't think it's 5.
ash2326
  • ash2326
What did you get when you plugged in x=5 ?
anonymous
  • anonymous
idk. i'm just trying to get this done. i'm so behind.
ash2326
  • ash2326
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
anonymous
  • anonymous
i got 1/3
ash2326
  • ash2326
Both sides?
anonymous
  • anonymous
yes. do you know the answer?
ash2326
  • ash2326
So 5 is the correct answer
anonymous
  • anonymous
do you know that it is?
ash2326
  • ash2326
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
anonymous
  • anonymous
What similarity statement can you write relating the three triangles in the diagram below?
anonymous
  • anonymous
1 Attachment

Looking for something else?

Not the answer you are looking for? Search for more explanations.