A) Height -7 = base
B) .5 * height * base = 60
Substituting A into B
B) .5 * height * (height -7) = 60
B) .5*height^2 -3.5*height = 60
B) .5*height^2 -3.5*height -60 = 0
Using the quadratic formula:
Height = 15
Subtracting 7 gives us the base length
Base = 8
**************************************************************
Double-Check
.5 * 15 * 8 = 60
Answer:
The area of the triangle is 18 square units.
Step-by-step explanation:
First, we determine the lengths of segments AB, BC and AC by Pythagorean Theorem:
AB
![AB = \sqrt{(5-2)^{2}+[6-(-1)]^{2}}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%285-2%29%5E%7B2%7D%2B%5B6-%28-1%29%5D%5E%7B2%7D%7D)
BC
AC
![AC = \sqrt{(-1-2)^{2}+[4-(-1)]^{2}}](https://tex.z-dn.net/?f=AC%20%3D%20%5Csqrt%7B%28-1-2%29%5E%7B2%7D%2B%5B4-%28-1%29%5D%5E%7B2%7D%7D)
Now we determine the area of the triangle by Heron's formula:
(1)
(2)
Where:
- Area of the triangle.
- Semiparameter.
If we know that , and , then the area of the triangle is:
The area of the triangle is 18 square units.
Answer: 110, 35, 70, G, J, F, E, B, A, H, C, D, I
Step-by-step explanation:
8. For number 8, you will be using the exterior angle theorem. The exterior angle theorem states that the exterior angle equals the two angles inside the given triangle. Since we have 50 and 60, you will add 50 + 60 to get 110.
9. In this problem, you shall use the vertical angle theorem. The vertical angle theorem is simply that any angles vertical from one another are congruent. So a will be also 35 degrees.
10. This is an image depicting two lines cut by a transversal, creating multiple congruent angles. With this, you will be using the alternate interior angle theorem. Alternate interior angles are angles on different sides of the transversal but inside both of the lines that were cut into, as shown above. So, b will also equal 70 degrees.
Part B:
1. G
2. J
3. F
4. E
5. B
6. A
7. H
8. C
9. D
10. I
This is quite basic actually,
208 kmh equals 208,000 meters per hour
This is because a km equates to 1000 meters.
