finding the dimensions?

Question

The pages of a textbook have uniform margins of 2 centimeters on all four sides. If the area of teh entire page is 480 square cenitmeters and the area of the printed proportion is 320 square centimeters, find the dimensions of the page.
how do you find the equation?
is it..
4(x+2)=800

Answer 1

Let the length and width of the entire page be x and y cm respectively
Therefore,
xy=480
length of the printed portion
=x-4 cm
Width of the printed portion
=y-4 cm
Therefore,
(x-4)(y-4)=320
=>xy-4x-4y+16=320
=>480-4(x+y)+16=320
=>-4(x+y)=320-480-16= -176
=>x+y= -176/-4=44..........(eqn 2)
we know that
(x-y)^2
=(x+y)^2-4xy
=(44)^2-4*480 [plugging the values of x+y and xy]
=1936-1920
=16
Hence x-y=4 [square-rooting both sides]
Now we have two simple linear equations
x+y=44 ,and
x-y=4
Solving them we get
x=24 cm and y=20 cm
Therefore the dimension of the page is 24cmx20 cm

Answer 2

We have L x B=480 sq cm
& (L-4)x(B-4)=320 sq cm
or LxB-4L-4B+16=320
or 480-4(L+B)+16=320
or -4(L+B)=320-480-16=-176
orL+B=-176/-4=44--------------(1)
Also (L-B)^2=(L+B)^2-4(LxB)
or(L-B)^2=44^2-4.480=1936-1920=16
or(L-B)^2=(4)^2
or L-B=4----------------------------(2)
From (1) & (2),we have
2L=48 or L=24,putting this value in(1),we have
24+B=44 or B=20,so L=24 &B=20 ans

Answer 3

The area of the printed page is 320 cm = x*y

The total page size is (x+4)*(y+4)=480

You can solve for x or y in the first equation and plug it into the other one to find the answer.

Answer 4

is the page a square or a rectangle ?
if it was a square the root of the area is the dimension

if it was a rectangle 2(x+y) = area
you should know x or y to solve it

if y =2
2(x+2)=480
x=238