The area of a garden is 900m^2 and has a perimeter of 0.2km. What are the dimensions of the garden?
why the silly mixture of units?
.2 km = 200 metres , so
width ---x
length --- y
xy = 900
2x+2y=200
x+y = 100 ---> y = 100-x
now sub into xy=900
x(100-x) = 900
expand, simplify and use the quadratic equation as in your other question.
let me know what you get
L*W = 900 m^2.
W = 900/L.
2L + 2W = 200 m.
Replace W with 900/L:
2L + 2(900/L) = 200,
L + 900/L = 100,
L^2 + 900 = 100L,
L^2 - 100L + 900 = 0,
L = (-B +- sqrt(B^2-4AC))/2A,
L = (100 +- sqrt(6400))/2 = 90m, and 10 m.
L = 90 m.
W = 900/L = 900/90 = 10 m.
l
62 - 100
l =
To find the dimensions of the garden, we can use the formulas for area and perimeter of a rectangle.
Let's assume that the length of the garden is L and the width of the garden is W.
The area of a rectangle is given by the formula: A = L * W.
Given that the area of the garden is 900m^2, we can write the equation:
900 = L * W ---(Equation 1)
The perimeter of a rectangle is given by the formula: P = 2 * (L + W).
Given that the perimeter of the garden is 0.2km, we need to convert it to meters (since the area is given in square meters) by multiplying it by 1000:
0.2km = 0.2 * 1000 = 200m
Now we can write the equation for the perimeter:
200 = 2 * (L + W) ---(Equation 2)
We have two equations (Equation 1 and Equation 2) and two unknowns (L and W), so we can solve the system of equations to find the dimensions of the garden.
Let's start by rearranging Equation 2 to solve for L:
200 = 2L + 2W
200 - 2W = 2L
100 - W = L ---(Equation 3)
Now substitute the value of L from Equation 3 into Equation 1:
900 = L * W
900 = (100 - W) * W
900 = 100W - W^2
W^2 - 100W + 900 = 0
We now have a quadratic equation. We can solve it by factoring or using the quadratic formula.
Using the quadratic formula: W = (-b ± √(b^2 - 4ac)) / (2a)
where a = 1, b = -100, and c = 900.
W = (-(-100) ± √((-100)^2 - 4 * 1 * 900)) / (2 * 1)
W = (100 ± √(10000 - 3600)) / 2
W = (100 ± √6400) / 2
W = (100 ± 80) / 2
So, W = (100 + 80) / 2 = 180 / 2 = 90m or W = (100 - 80) / 2 = 20 / 2 = 10m.
Now we can substitute the values of W back into Equation 3 to find the corresponding values of L:
For W = 90m, substituting in Equation 3, we get:
L = 100 - W = 100 - 90 = 10m
For W = 10m, substituting in Equation 3, we get:
L = 100 - W = 100 - 10 = 90m
Therefore, the dimensions of the garden are 90m by 10m.