The area of a. Front cover of a book is 120 square inches. The perimeter is 44 inches.what are the dimensions of the cover. HELP
2 L + 2 w = 44 so L + w = 22
L w = 120 so L = 120/w
120/w + w = 22
w^2 - 22w + 120 = 0
(w-12)(w-10) = 0
ten by 12 :)
the area of the front cover of a book
To find the dimensions of the book cover, you can use the formulas for area and perimeter of a rectangle. Let's denote the length as L and the width as W.
We are given the following information:
- Area: L * W = 120 square inches
- Perimeter: 2L + 2W = 44 inches
To start, let's use the area equation to find one of the variables in terms of the other.
L * W = 120
Next, let's use the perimeter equation to express one of the variables in terms of the other.
2L + 2W = 44
We can simplify the perimeter equation by dividing both sides by 2:
L + W = 22
Now, we can solve the perimeter equation for one of the variables, substitute this value into the area equation, and solve for the other variable.
Let's solve the perimeter equation for L:
L = 22 - W
Substitute this value into the area equation:
(22 - W) * W = 120
Expand the equation:
22W - W^2 = 120
Rearrange the equation:
W^2 - 22W + 120 = 0
This quadratic equation can be factored as follows:
(W - 12)(W - 10) = 0
This yields two potential values for W: 12 and 10.
Case 1: W = 12
If W = 12, then substituting W into the perimeter equation gives us: L = 22 - 12 = 10
Case 2: W = 10
If W = 10, then substituting W into the perimeter equation gives us: L = 22 - 10 = 12
Therefore, there are two possible dimensions for the book cover: 10 inches by 12 inches, or 12 inches by 10 inches.