SOLUTION: Susan, who is a graphic artist, is given a job to design a poster. This poster contains 70 square inches of type and pictures and has a uniform margin around the type of 2 inches.

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Question 947609: Susan, who is a graphic artist, is given a job to design a poster. This poster contains 70 square inches of type and pictures and has a uniform margin around the type of 2 inches. The height of the poster needs to be twice the width. What are the dimensions of the overall poster? (HINT: Usea calculator to figure out the square root if you use the quadratic formula.)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
h, height of poster
w, width of poster
u, uniform width or margin around the printing
A, area of printing on the poster
GIVEN:
h=2w
u=2
A=70

You should draw a picture of this (not shown in this solution).

Total poster area: h%2Aw.
Printed or typed area: %28h-2u%29%28w-2u%29=A, note how the dimensions of the printed area are less than the poster area.
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Notice that the unknown variables in that equation are h and w.

Simplify the Printed Area equation:
hw-2uw-2uh%2B4u%5E2-A=0
Substitute for h=2w.
2w%5E2-2uw-2u%2A2w%2B4u%5E2-A=0
2w%5E2-2uw-4uw%2B4u%5E2-A=0
highlight_green%282w%5E2-6uw%2B4u%5E2-A=0%29------you can continue this way symbolically and solve this quadratic equation for w, but you can also take advantage of your known even number value for A=70 NOW...

2w%5E2-6uw%2B4u%5E2-70=0
w%5E2-3uw%2B2u%5E2-35=0
and you also know u=2, so ...
w%5E2-6w%2B8-35=0
highlight_green%28w%5E2-6w-27=0%29-----Most convenient is to solve this equation for w. .... Factorable?

%28w-9%29%28w%2B3%29=0
The meaningful value is highlight%28w=9%29.
AND
highlight%28h=2w=18%29.