Answer:
Height: 9 in
Length: 6 in
Width: 4 in
Step-by-step explanation:
Given that A rectangular page is to contain 24 square inches
- Let y is the length of the rectangle
- Let x is the width of the rectangle
We know that:
The area of the the rectangle: A = length* width =24
<=> x*y = 24
<=> y = 24/x
As given in the question:
- Height (h) h = y + 2*1.5 <=> h = y + 3
- Lenght (l) = x + 2
<=> The area = h*l
= (y + 3 ) (x + 2
)
= (24/x+3) (x+2)
= 30 + 48 /x + 3x
Taking derivatives on both sides of the equation
A´(x) = -48/x² + 3
Let A´(x) = 0, we have:
-48/x² + 3 = 0
<=> x = 4 in
When x=4 in we have y = 24/4 = 6 and h = 6+3 = 9
=> A (min) = 6*9 = 54
So the dimensions are:
Height: 9 in
Length: 6 in
Width: 4 in
