What is the maximum length and width I can get with 300 flowers of around 1.5" in diameter if I want it to be rectangular but not square?

[Mackattack]

I'm making a blanket out of crocheted flowers sewn together. One flower is around 1.5 inches. There are 3 colors. Round off the number of flowers of each color to 100 each meaning, there are 300 in total. In order to keep the blanket straight and not slanting, the rows have to be:

X (where x is an even number of flowers)

X-1

This pattern repeats for the rest of the rows.

What is the maximum length and width I can achieve if I want it to be a rectangle but not a square? It's all right if a few flowers get left out in the final product for as long as the blanket is a full rectangle.

This is an old problem. In the end, I used 18 as my x and 17 as my odd since 289 is the closest square to 300. I remember solving a similar problem a few years back, but I don't remember how to solve it now hahaha!

 

[Otis]

Hello. If I'm understanding correctly, then nine 18-flower rows alternating with eight 17-flower rows would total 298 flowers. That is, the top and bottom rows contain 18 flowers.

298 flowers attached in such an arrangement would form a rectangle measuring about 27 inches by 25.5 inches.

Is it a cat blanket?

?

[imath]\;[/imath]

 

[lev888]

What is the maximum length and width

I don't think this is a valid question. If you want to use as many flowers as possible the area will be approximately 300. In such a rectangle as you increase length, width decreases. So, what exactly are we maximizing?

 

[Mackattack]

Hello. If I'm understanding correctly, then nine 18-flower rows alternating with eight 17-flower rows would total 298 flowers. That is, the top and bottom rows contain 18 flowers.

298 flowers attached in such an arrangement would form a rectangle measuring about 27 inches by 25.5 inches.

Is it a cat blanket?

?

[imath]\;[/imath]

Close! It was meant for my dog who until day still prefers sleeping on my slipper or the base of an electric fan.

 

[Mackattack]

I don't think this is a valid question. If you want to use as many flowers as possible the area will be approximately 300. In such a rectangle as you increase length, width decreases. So, what exactly are we maximizing?

You got a point. Let me clarify. What I really wanted was to maximize the area without it being a square. I just asked for length and width to get a rough visual.

 

[Cubist]

@Mackattack you could make a spreadsheet to try different options. You'll need two expressions:-

for even values of y the number of flowers will be \(\displaystyle y(2x-1)/2\)

for odd values of y the number of flowers will be \(\displaystyle (y(2x - 1) + 1)/2\)

A potential option, which is less square, would have used 297 flowers when x=14 and y=22

 

[Mackattack]

Thanks for the answers, everyone.