Answer:
Area = 2025 miles²
Perimeter = 180 miles
Step-by-step explanation:
Given the following :
Scale of drawing = 1 inch : 5 miles
Length of side of the scale drawing = 9 inches
To find The actual perimeter and area of the square, we need ;
Actual length of the drawing :
1 inch = 5 miles
9 inches = (5 × 9) miles = 45 miles
Hence,
Area of a square = a²
Where a = side length
Actual side length = 45 miles
Actual area of square = 45² = 2025 miles²
Actual Perimeter of square :
Perimeter of a square = 4a
a = side length
Actual perimeter = 4(45) = 180 miles
Answer:
7
Step-by-step explanation:
Answer: 1
Step-by-step explanation:
I assume you meant to type
.
By the Law of Sines,
![\frac{\sin C}{c}=\frac{\sin B}{b} \\ \\ \frac{\sin C}{18}=\frac{\sin 86^{\circ}}{21} \\ \\ \sin C=\frac{18 \sin 86^{\circ}}{21} \\ \\ C=\sin^{-1} \left(\frac{18 \sin 86^{\circ}}{21} \right), 180^{\circ}-\sin^{-1} \left(\frac{18 \sin 86^{\circ}}{21} \right) \\ \\ C \approx 58.77^{\circ}, 121.23^{\circ}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%20C%7D%7Bc%7D%3D%5Cfrac%7B%5Csin%20B%7D%7Bb%7D%20%5C%5C%20%5C%5C%20%5Cfrac%7B%5Csin%20C%7D%7B18%7D%3D%5Cfrac%7B%5Csin%2086%5E%7B%5Ccirc%7D%7D%7B21%7D%20%5C%5C%20%5C%5C%20%5Csin%20C%3D%5Cfrac%7B18%20%5Csin%2086%5E%7B%5Ccirc%7D%7D%7B21%7D%20%5C%5C%20%5C%5C%20C%3D%5Csin%5E%7B-1%7D%20%5Cleft%28%5Cfrac%7B18%20%5Csin%2086%5E%7B%5Ccirc%7D%7D%7B21%7D%20%5Cright%29%2C%20180%5E%7B%5Ccirc%7D-%5Csin%5E%7B-1%7D%20%5Cleft%28%5Cfrac%7B18%20%5Csin%2086%5E%7B%5Ccirc%7D%7D%7B21%7D%20%5Cright%29%20%5C%5C%20%5C%5C%20C%20%5Capprox%2058.77%5E%7B%5Ccirc%7D%2C%20121.23%5E%7B%5Ccirc%7D)
Since only one of these values will make a triangle (the obtuse possibility for C will mean
, which violates the condition that the angles of a triangle add to 180 degrees), 1 triangle can be formed.
Answer:
The following expression can be used to represent the perimeter of rectangle ABCD: 16x-12
Step-by-step explanation:
Let l be the length of rectangle and w be the width of rectangle.
Given that:
![l = 5x+1\\w = 3x-7](https://tex.z-dn.net/?f=l%20%3D%205x%2B1%5C%5Cw%20%3D%203x-7)
The perimeter of a rectangle is given by the expression:
![P = 2(l+w)](https://tex.z-dn.net/?f=P%20%3D%202%28l%2Bw%29)
Putting the values of length and width, we get
![P = 2\{(5x+1)+(3x-7)\}\\P = 2\{5x+1+3x-7\}\\P = 2(8x-6)\\P = 16x-12](https://tex.z-dn.net/?f=P%20%3D%202%5C%7B%285x%2B1%29%2B%283x-7%29%5C%7D%5C%5CP%20%3D%202%5C%7B5x%2B1%2B3x-7%5C%7D%5C%5CP%20%3D%202%288x-6%29%5C%5CP%20%3D%2016x-12)
Hence,
The following expression can be used to represent the perimeter of rectangle ABCD: 16x-12