SOLUTION: Here are a few problems that were given as a summer test in preparation for AP Calculus. I would appreciate it if I could recive soem help. The test is due tommorrow. Thank you i

Question 48653: Here are a few problems that were given as a summer test in preparation for AP Calculus. I would appreciate it if I could recive soem help. The test is due tommorrow. Thank you in advance for your help.
2. The three sides of a triangle are 9 inches, 11 inches, and 12 inches. Joining the midpoints of the sides of the original triangle forms a new triangle. Find the perimeter of the new triangle.
7. The hypotenuse of a right triangle is 15 inches, and the altitude upon the hypotenuse is 6 inches. Find the segme, ts of the hypotenuse.
8. A chord AB is 12 inches; E is its midpoint. Another chord, CD, 13 inches in length, cuts AB at E. Find CE and ED.
14. Find the circumference of a circle if an inscribed angle of 18 degrees intercepts an arc 6 inches long.
Thanks agian
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
2. The three sides of a triangle are 9 inches, 11 inches, and 12 inches. Joining the midpoints of the sides of the original triangle forms a new triangle. Find the perimeter of the new triangle.
-----------------------------------
Draw the picture.
Notice the three parallelograms you formby connecting the mid-points.
Each of the sides of the inner triangle is half of one of the outside sides.
Perimeter = 6+4.5+5.5=16
-----------------------------------------------
7. The hypotenuse of a right triangle is 15 inches, and the altitude upon the hypotenuse is 6 inches. Find the segme, ts of the hypotenuse.
Draw the picture.
The antitude forms two similar triangles.
The hypotenuse of the original triangle has two pieces: x and 15-x.
PROPORTION:
x/6=6/(15-x)
15x-x^2=36
x^2-15x+36=0
(x-3)(x-12)=0
x=3 inches ; 15-x=12 inches
--------------------------------
8. A chord AB is 12 inches; E is its midpoint. Another chord, CD, 13 inches in length, cuts AB at E. Find CE and ED.
-----------------------------------
Draw the picture.
You have formed two similar triangles because angle C and angle B
intercept the same arc, so are equal. Also angle A and angle D intercept
the same are, so are equal. And the vertical angles at E are equal.
So the triangles are similar.
Let CE=x, then ED = 13-x.
AE = 6 = EB
Proportion:
x/6 = 6/13-x
13x-x^2=36
x^2-13x+36=0
(x-9)(x-4)=0
x=9 then 13-x=4 or vice versa
-------------------------------
14. Find the circumference of a circle if an inscribed angle of 18 degrees intercepts an arc 6 inches long.
PROPORTION:
circumference/6 = 360 degrees/ 18 degrees
circum = 6(360/18)= 120 inches
----------------------------
Cheers
Stan H.

RELATED QUESTIONS
If you could help with this I would really appreciate it! A high school with 1000... (answered by ewatrrr)

ok, this is a big one. i need help with all of them, please and thank you. i wonder if i... (answered by Theo)

I am currently working on a summer homework packet for my Pre-Calculus class and there is (answered by MathLover1)

Okay. So we were given homework for summer. But there's one big problem. I don't remember (answered by ankor@dixie-net.com)

hello i am in 10th grade right now and we are learing about conics there are few... (answered by stanbon)

14b-21 _______ 15-10b This is an exercise for a test. I would very much... (answered by bucky)

Hello, I am a freshman student having problems in goemetry. It would be wonderful if I... (answered by jim_thompson5910)

Hi, I have the answers to the problems but I don't know the steps to get the answer here... (answered by jim_thompson5910)

Mary�s age is at least five more than twice her brothers age. Is it possible for Mary to... (answered by Boreal,solver91311)