What two numbers multiply to 56 and add to - 18?
1 answer:
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Answer:
80 m^2
Step-by-step explanation:
The given information lets you write two equations involving length (x) and width (y).
- 2(x +y) = 36 . . . . the perimeter is 36 m
- (x+1)(y+2) -xy = 30 . . . . increasing the length and width increases area
The second of these equations simplifies to another linear equation, giving a system of linear equations easily solved.
xy +y +2x + 2 -xy = 30
2x +y = 28 . . . . . . . subtract 2
Dividing the first equation by 2 gives
x +y = 18
and subtracting this from the above equation gives ...
(2x +y) -(x +y) = 28 -18
x = 10
Then
y = 18 -10 = 8
The area of the original rectangle is xy = 10·8 = 80 m^2.
The area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units
<h3>Perimeter and area of the triangle giving the equation of a line</h3>First we will plot the giving lines, determine the point of intersection and then use the Pythagoras theorem to determine the dimension of the right triangle.
From the given equation of the lines, the points of intersection of the line are (x₁, y₁) = (- 0.4, 5.2), (x₂, y₂) = (-0.8, 4.4) and (x₃, y₃) = (0, 4)
For the base
b² = c² -a²
b = √(-0.8)² + (4 - 4.4)²
b = 2√5 / 5
For the height
h = √((- 0.4) - (- 0.8))² + (5.2 - 4.4)²
height = 2√5 / 5
For the hypotenuse
r = √2 · b
r = 2√10 / 5
<h3>Determine the Perimeter and area</h3>Perimeter = s1+s2+s3
Perimeter = 2√5 / 5 + 2√5 / 5 + 2√10 / 5
Perimeter = (2√10 + 4√5) / 5 units
<u>For the area</u>
area = 1/2* base * height
A = 0.5 · (2√5 / 5) · (2√5 / 5)
A = 2/5 square units
Hence the area and perimeter of the triangle is 2/5 square units and (2√10 + 4√5) / 5 units
Learn more on area and perimeter of triangles here: brainly.com/question/21511715
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