# A poster is to have an area of 630 cm2 with 2.5 cm margins at the bottom and sides and a 5 cm margin at the top. Find the exact dimensions (in cm) that will give the largest printed area.

The largest printed area for a poster with an area of 630 cm2 and 2.5 cm margins at the bottom and sides, and a 5 cm margin at the top is 58.5 cm x 10.75 cm. To find this exact dimension, we need to solve an equation using algebraic measures:

## A poster is to have an area of 630 cm2 with 2.5 cm margins at the bottom and sides and a 5 cm margin at the top. Find the exact dimensions (in cm) that will give the largest printed area.

Area = (width + 2(2.5)) * (length + 5)

630 = (w + 5) * (l + 5).

Rearranging this equation yields l = 12.25 – (w/10) , which can be substituted into the original equation to give:

630 = w*12.25 – w^2/10.

We can then use quadratic equation formula to solve for w; doing so gives us two solutions, one being negative and thus not possible for dimensions of a rectangle:

w= 11 or w= 58.50.
< br >Therefore, substituting these values into our original equations yields that the largest printed area has dimensions of 58.50cm x 10.75cm

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