A map of the world has an area of 28 square feet. Its perimeter is 22 feet. What are the dimensions of the map?
A = LW
The area could be
4 * 7
Do those dimensions give a perimeter of 22 feet?
To find the dimensions of the map, we can set up a system of equations using the given information.
Let's assume the length of the map is x feet, and the width of the map is y feet.
From the given information, we know that the area of the map is 28 square feet, so we have the equation:
x * y = 28 (equation 1)
We also know that the perimeter of the map is 22 feet, which can be written as:
2 * (x + y) = 22 (equation 2)
To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.
From equation 1, solve for y:
y = 28 / x
Now substitute this value of y into equation 2:
2 * (x + 28 / x) = 22
Multiply through by x to eliminate the fraction:
2x^2 + 56 = 22x
Rearrange the equation:
2x^2 - 22x + 56 = 0
Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula. Let's use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
In this case, a = 2, b = -22, and c = 56.
Plugging in the values:
x = (-(-22) +/- sqrt((-22)^2 - 4 * 2 * 56)) / (2 * 2)
Simplifying the expression under the square root:
x = (22 +/- sqrt(484 - 448)) / 4
x = (22 +/- sqrt(36)) / 4
Taking the square root:
x = (22 +/- 6) / 4
x = (22 + 6) / 4 or x = (22 - 6) / 4
x = 28 / 4 or x = 16 / 4
x = 7 or x = 4
Now substitute the values of x back into equation 1 to find y:
For x = 7:
7 * y = 28
y = 28 / 7
y = 4
And for x = 4:
4 * y = 28
y = 28 / 4
y = 7
So, the dimensions of the map are 7 feet by 4 feet or 4 feet by 7 feet.
To find the dimensions of the map, we can set up a system of equations using the given information.
Let's assume the length of the map is x feet and the width is y feet.
We have two equations:
1. The area of the map is given by: x * y = 28
2. The perimeter of the map is given by: 2 * (x + y) = 22
Now, we can solve this system of equations:
From equation 2, we can simplify it to: x + y = 11.
Then, we can isolate one variable in terms of the other. Let's isolate y by subtracting x from both sides: y = 11 - x.
Now, substitute this value of y into equation 1:
x * (11 - x) = 28
Expand and rearrange the equation to obtain a quadratic equation:
11x - x^2 = 28
x^2 - 11x + 28 = 0
At this point, we can solve the quadratic equation either by factoring or using the quadratic formula. Since the equation factors easily, let's factor it as:
(x - 4)(x - 7) = 0
Now, we have two possible solutions:
1. x - 4 = 0 --> x = 4. If x = 4, then y = 11 - 4 = 7.
2. x - 7 = 0 --> x = 7. If x = 7, then y = 11 - 7 = 4.
Therefore, the dimensions of the map could be 4 feet by 7 feet or 7 feet by 4 feet.