SOLUTION: A page with length 3 cm longer than its width has 80 cm^2 of printed area. The margins at the top and bottom are each 3/2 cm and the side margins are each 1 cm. Find the dimensions

Algebra ->  Rectangles -> SOLUTION: A page with length 3 cm longer than its width has 80 cm^2 of printed area. The margins at the top and bottom are each 3/2 cm and the side margins are each 1 cm. Find the dimensions      Log On


   

Question 983408: A page with length 3 cm longer than its width has 80 cm^2 of printed area. The margins at the top and bottom are each 3/2 cm and the side margins are each 1 cm. Find the dimensions of the page.
Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let width of page be x
length of page = (x+3)
width of painted area = (x-2) cm
length of printed area = (x+3)-3 = x
x(x-2) = printed area
x^2-2x = 80
x^2=10x+8x=80
x^2-10x+8x-80=0
x(x-10)+8(x-10)=0
(x+8)(x-10)=0
x= -8 OR 10 ( ignore negative)
width of page = 10cm
length of page = 13 cm


Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
w for width
L for length

L=w%2B3
Length of printing, L-2%2A1
Width of printing, w-2%283%2F2%29=w-3

Printed Area, %28L-2%29%28w-3%29=80
Substitute for L.
%28w%2B3-2%29%28w-3%29=80
%28w%2B1%29%28w-3%29=80
w%5E2-2w-3-80=0
highlight_green%28w%5E2-2w-83=0%29-----not seem factorable.

Discriminant: 4%2B4%2A83=336
336=12%2A28=2%2A2%2A3%2A4%2A7=2%5E4%2A3%2A7=2%5E4%2A21

w=%282%2B-+sqrt%282%5E4%2A21%29%29%2F2
w=%282%2B-+4%2Asqrt%2821%29%29%2F2
w=1%2B-+2sqrt%2821%29
Only the PLUS form can be accepted.
highlight%28highlight%28w=1%2B2sqrt%2821%29%29%29
Find L from this value for w.