find the dimension of the page.

Question

the area of the page of a book is 40 square inches, the area of the printed part is 21 7/8 square inches. the margin at the top and sides is 3/4 inch wide, the margin at the bottom is 1 inch wide. find the dimension of the page.

Answer 1

Emilyn---

I am going to give you another example to work with.

 

Suppose a landscaper is trying to determine the total area of a back yard. The entire backyard is covered by a pool (with dimensions 25'X50') and a sidewalk that extends out from the pool on each side by 6'. What is the total area of the back yard?

 

To solve this, you must realize that you are working with a rectangular pool. Two sides will have length of 25' and two will have length of 50'.

 

I wish I could draw this out for you so that you can see it here. However, that is not possible, so try looking at this diagram http://www.bing.com/images/search?q=pool+and+sidewalk+math+problem&qs=n&form=QBIR&pq=pool+and+sidewalk+math+problem&sc=0-0&sp=-1&sk=#view=detail&id=2295AE20EBF9C540ACBBC13B3594EF2EF451A8A8&selectedIndex=0

 

(If you cannot see the image, let me know.)

 

Looking at the left hand side of the pool, we have 25' in length. However, we must add the 6' sidewalk to that length to find its total. Many students will try to say that 25+6=31, but in fact, the sidewalk is on BOTH sides of the pool, so you must say that 25+6+6=37.

 

37 will be the width of the backyard.

 

You can use this same method to find the length of the backyard.

 

Multiply the two together to find the total area covered.

 

Let me know if you need clarification on any of this!!!

Answer 2

page is x by y inches.

 

xy = 40; y = 40/x

 

21 7/8 = (x-3/2)(y-3/4-1)

 

21 7/8 = (x-3/2)(40/x–7/4)

 

21 7/8 = (1/2)(2x-3)(1/(4x))(160–7x)

 

Multiply both sides by 8x:

 

x(168 + 7) = (2x–3)(160–7x)

 

175x = -14x^2+320x+21x-480

 

14x^2 - (341 - 175)x + 480 = 0

 

14x^2 – 166x + 480 = 0

 

7x^2 – 83x + 240 = 0

 

a(x-h)^2+k = ax^2–2ahx+ah^2+k

 

h = 83/14

 

k = 240 – 7*(83/14)^2 = 240 – 83*83/(2*14)

 

k = (240*2*14 – 83*83)/(2*14) = -169

 

7(x–83/14)^2 = 169 = 13^2

 

| x–83/14 | = 13/√(7)

 

x = 83/14 ± 13/√(7)

 

x = 3.28282011750684 or 8.57432273963602

 

y = 40/x = 12.18464569127177 or 4.6650914847296

 

Two possibilities: 3.3 by 12.2 or 8.6 by 4.7