Aposter is to have an area of 180 in2 with 1 inch margins at the bottom and sides and a 2 inch margin at the top. find the exact dimensions that will give the largest printed area.

x = 2√30

y= 3√30

Step-by-step explanation:

Area= 180in^2

For the larger shape,

Let the length be x and the width be y

A = x. y

x. y = =180

y= 180/x

For the smaller shape, lenght= x-2 while width = y-3

Area = (x-2)(y-3)

A(x) = (x-2)(y-3)

Put y= 180/x into A(x)

= (x-2)(180/x -3)

= 180 - 3x - 360/x + 6

Differentiate A(x) with respect to x

A'(x) = -3x+ 360/x^2

A'(x) = 0

0 = -3x + 360/x^2

3x = 360/x^2

3x^3 = 360

x^3 = 360/3

x^3 = 120

x = cuberoot 120

x = 2√30

Recall that y= 180/x

y = 180/2√30

y= 90/√30

By rationalizing the surd, we have

y = 90/√30 * √30/√30

y = (90√30) /30

y = 3√30

x = 2√30, y = 3√30