Algebra 2 help!! Find the value of k
1 answer:
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Answer:
216 people
Step-by-step explanation:
Given:
2.5 feet² is occupied by 1 person
Dimension of room = 216 in × 360 in
Required:
No. of people that would occupy the room
SOLUTION:
Step 1:
Convert the dimensions of the room from in to ft
Note: 1 foot = 12 inches
216 inches =
360 inches =
Step 2: calculate area of the room.
Area of the room = 30*18 = 540 ft²
Step 3: calculate the no. of people the room will contain.
2.5 ft² will contain one person
Therefore, 540 ft² will contain:
Check the picture below.
so notice, the sides AB and AC you can pretty much count them off the grid.
now, to get the CB side.
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) C&({{ -5}}\quad ,&{{ 1}})\quad % (c,d) B&({{ 3}}\quad ,&{{ -5}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ CB=\sqrt{[3-(-5)]^2+[-5-1]^2}\implies CB=\sqrt{(3+5)^2+(-5-1)^2} \\\\\\ CB=\sqrt{8^2+(-6)^2}\implies CB=\sqrt{100}\implies CB=10](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AC%26%28%7B%7B%20-5%7D%7D%5Cquad%20%2C%26%7B%7B%201%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0AB%26%28%7B%7B%203%7D%7D%5Cquad%20%2C%26%7B%7B%20-5%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0ACB%3D%5Csqrt%7B%5B3-%28-5%29%5D%5E2%2B%5B-5-1%5D%5E2%7D%5Cimplies%20CB%3D%5Csqrt%7B%283%2B5%29%5E2%2B%28-5-1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0ACB%3D%5Csqrt%7B8%5E2%2B%28-6%29%5E2%7D%5Cimplies%20CB%3D%5Csqrt%7B100%7D%5Cimplies%20CB%3D10)
sum all three sides up, and that's the perimeter of the triangle.
so notice, the sides AB and AC you can pretty much count them off the grid.
now, to get the CB side.
sum all three sides up, and that's the perimeter of the triangle.