Answer:
Base = 10 cm
Height = 60 cm
Step-by-step explanation:
The formula for the area of a triangle is
, where <em>b</em> is the length of the base of the triangle, and <em>h</em> is the length of the height of the triangle.
We know the area is 300, and since the height of the triangle is 6 times its base, we know that
. We can plug in these values into our formula for the area of a triangle, which gives us the following equation to solve:
![300=\frac{1}{2} *b*(6*b)](https://tex.z-dn.net/?f=300%3D%5Cfrac%7B1%7D%7B2%7D%20%2Ab%2A%286%2Ab%29)
![3b^2=300](https://tex.z-dn.net/?f=3b%5E2%3D300)
![b=\sqrt{100} =10](https://tex.z-dn.net/?f=b%3D%5Csqrt%7B100%7D%20%3D10)
The base of the triangle is 10 centimeters.
Now that we know the base of the triangle, we can plug its value in to the original formula to solve for the height of the triangle, which gives us the following equation:
![300=\frac{1}{2} *10*h](https://tex.z-dn.net/?f=300%3D%5Cfrac%7B1%7D%7B2%7D%20%2A10%2Ah)
![5h=300](https://tex.z-dn.net/?f=5h%3D300)
![h=60](https://tex.z-dn.net/?f=h%3D60)
The height of the triangle is 60 centimeters.
Please consider the attached file.
We can see that triangle JKM is a right triangle, with right angle at M. Segment KM is 6 units and segment MJ is 3 units. We can also see that KJ is hypotenuse of right triangle.
We will use Pythagoras theorem to solve for KJ as:
![KJ^2=KM^2+MJ^2](https://tex.z-dn.net/?f=KJ%5E2%3DKM%5E2%2BMJ%5E2)
![KJ^2=6^2+3^2](https://tex.z-dn.net/?f=KJ%5E2%3D6%5E2%2B3%5E2)
![KJ^2=36+9](https://tex.z-dn.net/?f=KJ%5E2%3D36%2B9)
![KJ^2=45](https://tex.z-dn.net/?f=KJ%5E2%3D45)
Now we will take positive square root on both sides:
![\sqrt{KJ^2}=\sqrt{45}](https://tex.z-dn.net/?f=%5Csqrt%7BKJ%5E2%7D%3D%5Csqrt%7B45%7D)
![KJ=\sqrt{9\cdot 5}](https://tex.z-dn.net/?f=KJ%3D%5Csqrt%7B9%5Ccdot%205%7D)
![KJ=3\sqrt{5}](https://tex.z-dn.net/?f=KJ%3D3%5Csqrt%7B5%7D)
Therefore, the length of line segment KJ is
and option D is the correct choice.
Someone better come get her because she dancing like a s.t.i.p.p.e.r
Answer:
14 deliveries per hour
Step-by-step explanation:
42/3
14
The person makes 14 deliveries per hour