Marlene D.

asked • 06/14/19# Please help me with my math

A graphics printing company sells three different sizes of posters. They use all of a 33”by 33” poster board and cut it into three pieces. The smallest one is a square, and the largest one will have three times the area of the middle-sized one. What are the dimensions of the three sizes of posters?

## 2 Answers By Expert Tutors

Patrick B. answered • 06/15/19

Math and computer tutor/teacher

The smallest square has side measure y.

Then the medium square has dimensions y and 33-y

The largest piece has dimensions 33-y and 33.

The area of the smallest piece is y^2

the area of the middle piece is y(33-y)

the area of the largest piece is 33(33-y)

3 * area of middle = area of largest

3 y (33-y) = 33(33-y)

divides both sides by 3(33-y) provided that y is not 33 gives

y = 11

Smallest piece is 11 by 11.

Middle piece is 11 x 22 and has area 242

the largest piece is 22 by 33 and has area 726 which is 3 times as large

Mark H. answered • 06/14/19

Tutoring in Math and Science at all levels

First, recognize that the square must be in one corner, and that the other two shapes are defined by extending one side of the square. Thus, the largest piece is a rectangle whose longest side is 33.

DRAW A PICTURE to see all of this.

Next, assign the variable X to the sides of the square.

Notice that each rectangle has one side that is 33 - X. For the ratio of areas to be the same, the ratio of the other sides must also be 3

The rectangles are X * (33 - X), and 33 * (33 - X). So, 3X = 33, and X = 11

The three sections are then:

11 * 11

22 * 11

22 * 33

Summing the areas: 121 + 242 + 726 = 1089 ( which is 33^{2} )

Again: __Draw a Picture__

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Mark M.

06/14/19