Answer: Approximately 72.69 meters
Step-by-step explanation:

Answer:
Step-by-step explanation:
AB^2 = HB^2 + AH^2 => AB = 15cm
Ta co cong thuc: 1/AH^2 = 1/AB^2 + 1/AC^2 => AC=20cm
Vay SABC= 1/2 .AB.AC = 1/2 .15.20=150cm^2
Answer:
the base is 9/2 ft and the height is 9/2 + 8, or 25/8, ft.
Step-by-step explanation:
Note that the formula for the area of a triangle is A = (1/2)(base)(height). Let's abbreviate that to A = (1/2)(b)(h). We are told that h = b + 8.
Then A = 136.5 = (1/2)(b)(b + 8), or
(after multiplying both sides by 2)
A = 273 = b^2 + 8b
which, when put into standard quadratic form, becomes:
b^2 + 8b - 273 = 0
The coefficients of this quadratic are a = 1, b = 8 and c = -273.
Thus, the discriminant is b^2 - 4ac, or 64 - 4(1)(-273) = 1156 = 17^2.
The roots are then
-8 ± √1156 -8 ± 17
x = -------------------- = ------------ = 9/2 and -25/2
2 2
Only the root 9/2 makes sense here, because measurements of length are positive.
Thus, the base is 9/2 ft and the height is 9/2 + 8, or 25/8, ft.
Answer:
60
Step-by-step explanation:
What we know:
- ABD is a straight angle, it measures 180 degrees
- Angle CBA + CBD = 180 degrees
- Angle GFH = CBA (they are alternate exterior angles)
Equation:
GFH + CBD = 180
Substitute:
3x + 6x = 180
Add:
3x + 6x = 180
9x = 180
Divide:
9x = 180
/9 /9
x = 20
Substitute:
GFH = 3x
GFH = 3(20)
GFH = 60
m<GFH is 60°
You have the correct answer. Nice work. If you need to see the steps, then see below
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First we need to find the midpoint of H and I
The x coordinates of the two points are -4 and 2. They add to -4+2 = -2 and then cut that in half to get -1
Do the same for the y coordinates: 2+4 = 6 which cuts in half to get 3
So the midpoint of H and I is (-1,3). The perpendicular bisector will go through this midpoint
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Now we must find the slope of segment HI
H = (-4,2) = (x1,y1)
I = (2,4) = (x2,y2)
m = (y2 - y1)/(x2 - x1)
m = (4 - 2)/(2 - (-4))
m = (4 - 2)/(2 + 4)
m = 2/6
m = 1/3
Flip the fraction to get 1/3 ---> 3/1 = 3
Then flip the sign: +3 ----> -3
So the slope of the perpendicular bisector is -3
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Use m = -3 which is the slope we found
and (x,y) = (-1,3), which is the midpoint found earlier
to get the following
y = mx+b
3 = -3*(-1)+b
3 = 3+b
3-3 = 3+b-3
0 = b
b = 0
So if m = -3 and b = 0, then y = mx+b turns into y = -3x+0 and it simplifies to y = -3x
So that confirms you have the right answer. I've also used GeoGebra to help confirm the answer (see attached)