Answer:
C. 12m
Explanation:
Let the length of the shorter arm = x
Since the length of the longer arm is equal to twice the length of the shorter arm;
• The length of the longer arm = 2x
• The area of triangle ABD = 18√3 m².
Given a triangle with two sides and the included angle, the area of the triangle is calculated using the formula below:
![\begin{gathered} \text{Area}=\frac{1}{2}ab\sin \theta \\ \implies\text{Area of triangle ABD =}\frac{1}{2}bd\sin A \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7BArea%7D%3D%5Cfrac%7B1%7D%7B2%7Dab%5Csin%20%5Ctheta%20%5C%5C%20%5Cimplies%5Ctext%7BArea%20of%20triangle%20ABD%20%3D%7D%5Cfrac%7B1%7D%7B2%7Dbd%5Csin%20A%20%5Cend%7Bgathered%7D)
Therefore:
![18\sqrt[]{3}=\frac{1}{2}(x)(2x)\sin (60\degree)](https://tex.z-dn.net/?f=18%5Csqrt%5B%5D%7B3%7D%3D%5Cfrac%7B1%7D%7B2%7D%28x%29%282x%29%5Csin%20%2860%5Cdegree%29)
We solve for x.
![\begin{gathered} 18\sqrt[]{3}=\frac{2x^2}{2}\times\sin 60\degree \\ 18\sqrt[]{3}=x^2\times\frac{\sqrt[]{3}}{2} \\ \text{Multiply both sides by }\frac{2}{\sqrt[]{3}} \\ 18\sqrt[]{3}\times\frac{2}{\sqrt[]{3}}=x^2\times\frac{\sqrt[]{3}}{2}\times\frac{2}{\sqrt[]{3}} \\ x^2=36 \\ x^2=6^2 \\ x=6 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2018%5Csqrt%5B%5D%7B3%7D%3D%5Cfrac%7B2x%5E2%7D%7B2%7D%5Ctimes%5Csin%2060%5Cdegree%20%5C%5C%2018%5Csqrt%5B%5D%7B3%7D%3Dx%5E2%5Ctimes%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%20%5C%5C%20%5Ctext%7BMultiply%20both%20sides%20by%20%7D%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%2018%5Csqrt%5B%5D%7B3%7D%5Ctimes%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%3Dx%5E2%5Ctimes%5Cfrac%7B%5Csqrt%5B%5D%7B3%7D%7D%7B2%7D%5Ctimes%5Cfrac%7B2%7D%7B%5Csqrt%5B%5D%7B3%7D%7D%20%5C%5C%20x%5E2%3D36%20%5C%5C%20x%5E2%3D6%5E2%20%5C%5C%20x%3D6%20%5Cend%7Bgathered%7D)
Multiply x by 2 to get the length of the longer arm:
![2x=2\times6=12m](https://tex.z-dn.net/?f=2x%3D2%5Ctimes6%3D12m)
The length of the longer arm is 12m.
C is the correct option.
Answer:
<em>(a) 3 inches
</em>
<em>(b) Her scale model drawing WILL fit on the piece of paper 8.5 by 7 inches</em>
Step-by-step explanation:
<u>Scaling
</u>
We use scales to represent realities in reduced spaces. In the case of lengths or surfaces, the scale allows us to draw the shapes in normal sheets of paper.
(a)
Kelly's rock garden has a length of 6 feet. She uses a 1 inch:2 feet scale. this means that the model length is
6 feet*1 inch/2 feet = 3 inches
(b)
The width of the model is 5 inches, keeping the same scale it means the real length is
5 inches * 2 feet / 1 inch = 10 feet
The model will have 3 inches by 5 inches, it perfectly fits on any regular piece of paper
Answer:
Dark chocolate = 1 pound
Step-by-step explanation:
I have no idea what I'm supposed to find but if its the amount of dark chocolate then its 1.
Answer:
the correct answer is 6x^4