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.
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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
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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
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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.
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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
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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
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Cheers
Stan H.
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