Please help me answer this I just want some help.

Question

A graphics printing company sells three different sizes of posters. They use all of a 36” by 36” 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? 

Answer 1

Smallest area is x².

 

A₁ = x²

 

Presumably, all posters are rectangles. There is only one way to allow this to happen, in terms of x:

 

A₂ = x(36-x)

A₃ = 36(36-x)

 

It is a bit hard without a diagram... I guess you could think of the flag of U.S.A. The blue with stars would be the square, the short stripes would correspond to one rectangle, and the long stripes correspond to a big rectangle. There is some minuscule chance the following will format appropriately on your screen:

______________________

|              |                                   |

|     A1    |            A2                  |

|______|_______________|

|                                                  |

|                                                  |

|                      A3                       |

|                                                  |

|                                                  |

|_____________________|

 

 

Anyway, the problem says the largest is 3 times bigger than the middle-sized.

 

36(36-x) = 3x(36-x)

 

Assuming x is not 36, we can divide by (36-x).

 

36 = 3x

 

Divide by 3.

 

x = 12

 

So, the dimensions are 12" x 12", 12" x 24", and 36" x 24".