There are three answers and they are: choice 2, choice 3, choice 5
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Further Explanation:
Choice 1 is false because the intersection of the altitudes of a triangle leads to the orthocenter.
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Choice 2 is true because the three medians of any triangle always intersect at the centroid. A median is a line that goes from one vertex to the midpoint of the opposite side. In this case, we go from point E to the midpoint of side CD. The midpoint of CD is found by bisecting segment CD (see choice 5)
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Choice 3 is true. This is effectively the same as choice 5 below. The "perpendicular" aspect does not matter.
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Choice 4 is false. Following the steps mentioned here will create an altitude line (see choice 1)
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Choice 5 is true. To bisect something is to cut it in half. Let's say that point F is the midpoint of line segment CD. This means that line segment EF is one of the three medians of triangle CDE.
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edit update: I changed choice 3 from false to true
Answer:
3/2
Step-by-step explanation:
A - age of Abigail
C - age of Cynthia
A = C + 8
A - 20 = 3 (C - 20)
A - 20 = 3C - 60
C + 8 - 20 = 3C - 60
C - 12 = 3C - 60 A = C + 8
2C = 48 A = 24 + 8
C = 24 years A = 32 years
Distribute the 3a^n to all the other values then solve...
(3a^n*a^n)+(3a^n*a^n)+(3a^n*-1)
4a^2n+4a^2n-3a^n=
8a^2n-3a^n
In order to begin we must start off with the formula for the area of a triangle, which is a=1/2b(h) where a is area, b is base, and h is height.
In this scenario, we know that the area is 45cm^2 and the base is 2h+12 (since it is twice it’s height plus twelve). We can plug this into the area equation and then proceed to solve out accordingly.
a=1/2b(h)
45=1/2(2h+12)(h)
90=(2h+12)(h)
90=2h^2 + 12h
0= 2h^2 + 12h - 90
Simplify by dividing the two out.
h^2 + 6h - 45 = 0.
Now plug into the quadratic formula (with a=1, b=6, and c=-45) as shown in the image below.
After plugging the equation in and solving, we come to the idea that h is roughly equal to 4.34. We can now plug this back into the triangle area formula to solve out for b.
a=1/2b(h)
45=1/2(2h + 12)(h)
45=1/2(20.69)(4.34)
45=45.
In conclusion;
The height is ≈ 4.34
The base is ≈ 8.68
Hope this helps :)
