Answer: Angle A = 120° and angle C = 45°
Step-by-step explanation: The first thing to note at the back of our minds is that the sum of the interior angles of a triangle equals 180°. Given that the three angle are available, we can start by adding them all together. Hence,
{12x + 12} + 15 + {3x + 18} = 180
12x + 12 + 15 + 3x + 18 = 180
By collecting like terms, we arrive at,
12x + 3x + 12 + 15 + 18 = 180
15x + 45 = 180
Subtract 45 from both sides of the equation
15x = 135
Divide both sides of the equation by 15
x = 9
At this point, we can now substitute for the value of x = 9 in the expressions representing angles A and C.
Angle A = 12x + 12
= 12(9) + 12
= 108 + 12
= 120
Angle A = 120°
Angle C = 3x + 18
= 3(9) + 18
= 27 + 18
= 45
Angle C = 45°
Answer:
Step-by-step explanation:
130+5x=180
130-130+5x=180-130
5x=50
x=10
Answer:
The total Perimeter of the pitch and seating area is 179.83 m an the Total Area is 1394 m²
Step-by-step explanation:
Figure is attached with required naming.
Length of the Rectangle 1 = 40 m
width of the Rectangle 2 = 2000 cm = 20 m
radius of semi circle 2 =
radius of semi circle 3 =
length of the rectangle 4 = 25 m
width of the rectangle 4 = 800 cm = 8 m
length of the rectangle 5 = 10 m
width of the rectangle 5 = 800 cm = 8 m
Total Perimeter of the pitch and seating area
= length of rectangle 1 + circumference of semi circle 2 + circumference of semi circle 3 + length of rectangle 4 + 2 × width of rectangle 4 + length of rectangle 5 + 2 × width of the rectangle 5 + (length of rectangle 1 - length of rectangle 4 - length of he rectangle 5)
= 40 + π(10) + π(10) + 25 + 2 × 8 + 10 + 2 × 8 + ( 45 - 25 -10 )
= 40 + π(10) + π(10) + 25 + 16 + 10 + 16 + 10
= 117 + 20π
= 179.83 m (approx.)
Total area of the pitch and seating area
= Area of the Rectangle 1 + Area of semi circle 2 + area of semi circle 3 + area of rectangle 4 + area of rectangle 5
= 40 × 20 + π(10)² + 25 × 8 + 10 × 8
= 800 + 100π + 200 + 80
= 1080 + 314
= 1394 m²
Therefore, The total Perimeter of the pitch and seating area is 179.83 m an the Total Area is 1394 m²
Answer:
Expression: 3.5((12x18) + 13²)
Step-by-step explanation:
Since George is going to put carpeting in two different rooms, one rectangular and one square, you need to find the area of each room, add the sum and then multiply the total area needed by the cost per square foot of carpet. The area of a rectangle is: a = lw, where l=length and w = width. The area of a square is: a = s², where s = side of the square. Take the sum of these two areas would be (12 x 18) + 13² or 213 + 169 = 382. Since the cost of the carpet is the same per square foot, you can multiply the entire sum by the cost of $3.50 or: 3.5((12 x 18) + 13²) or 3.5(382) = $1,337.
