A rectangular table top has a perimeter of 22 inches and an area of 28 square inches. Find its dimensions.
Answer is 4,7
To find the dimensions of the rectangular table top, we'll use the given information that its perimeter is 22 inches and its area is 28 square inches.
Let's denote the length of the table as L and the width as W.
1. Perimeter: The perimeter of a rectangle is calculated by adding together all four sides. In this case, we have two sides of length L and two sides of length W. So, the perimeter equation is: Perimeter = 2L + 2W.
2. Area: The area of a rectangle is found by multiplying its length by its width. In this case, the area equation is: Area = L * W.
Given that the perimeter is 22 inches, we can rewrite the perimeter equation as: 2L + 2W = 22.
Similarly, given that the area is 28 square inches, we can rewrite the area equation as: L * W = 28.
Now we have a system of two equations with two variables. Let's solve it to find the values of L and W.
From the perimeter equation, we can isolate L by subtracting 2W from both sides: 2L = 22 - 2W.
Next, divide both sides by 2 to solve for L: L = (22 - 2W) / 2.
Now substitute the value of L in the area equation: (22 - 2W) * W = 28.
Expand the equation: 22W - 2W^2 = 28.
Rearrange the equation in quadratic form: 2W^2 - 22W + 28 = 0.
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use factoring for this example.
Factor the equation: (2W - 4)(W - 7) = 0.
Set each factor equal to zero and solve for W:
1) 2W - 4 = 0 -> 2W = 4 -> W = 2.
2) W - 7 = 0 -> W = 7.
Since the width cannot be negative, we discard the W = 7 solution.
Now that we have the value of W, we can substitute back into the perimeter equation to find L.
Using L = (22 - 2W) / 2:
L = (22 - 2*2) / 2 -> L = 18 / 2 -> L = 9.
Therefore, the dimensions of the rectangular table top are: Length = 9 inches, Width = 2 inches.
Factors of 28
2, 14
4, 7
Which of those pairs will give you a perimeter of 22?