Beth has three books. The cover of the first book has an area of 20 in 2 . The cover of the second book has an
area of x in2, and the cover of the third book has an area of 88 in2. The area of the third cover is the same as a rectangle whose width is the side width of the first cover and whose length is the side length of the second cover.
Write and solve an equation using the properties of rational exponents to find the side width of the second book’s cover. Round to the nearest tenth, if necessary.
The area of the third cover is equal to the product of the width and length of the rectangle.
Let the width of the first book's cover be w inches.
Let the length of the second book's cover be l inches.
The area of the first book's cover can be expressed as w^2 = 20.
The area of the third book's cover can be expressed as lw = 88.
To find the side width of the second book's cover, we need to solve for l.
From the equation w^2 = 20, we can take the square root of both sides to solve for w: w = √20 ≈ 4.47.
Plugging this value into the equation lw = 88, we get:
4.47l = 88
Dividing both sides by 4.47, we find:
l ≈ 19.7
Therefore, the side width of the second book's cover is approximately 19.7 inches.
Let's solve for the side width of the second book's cover.
Given:
Area of the first book's cover = 20 in^2
Area of the third book's cover = 88 in^2
We are told that the area of the third cover is the same as a rectangle whose width is the side width of the first cover and whose length is the side length of the second cover.
Let's assume the side width of the second book's cover is w inches.
So, the area of the third cover is given by: length * width = w * x
Given that the area of the third cover is 88 in^2, we can write the equation as:
w * x = 88
Now let's solve the equation for x:
x = 88 / w
We also know that the area of the first book's cover is 20 in^2.
The area of the first cover is given by: side width * side width = w^2
So, w^2 = 20
To solve for w, we can take the square root of both sides:
√w^2 = √20
w = √20
Now substitute this value of w in the equation we derived earlier:
x = 88 / √20
Simplifying this expression:
x ≈ 18.63
Therefore, the side width of the second book's cover is approximately 18.63 inches.