# Proportions

• Jan 26th 2009, 05:58 PM
Startbucks
Proportions
1.) Given that:

Picture A has width $605$ pixels, and height $693$ pixels

Picture B has width $775$ pixels, and height $546$ pixels,

without distorting either of the pictures (so you have to change height/width by the same proportion), make the taller picture the same height as the other picture. Determine which picture to change and determine how you'll alter the dimensions.

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2.) Suppose you are placing these pictures on a site that's only $630$ pixels wide. After insuring the pictures are the same height, you find out that they are too wide to fit on the site next to each other. Again, without distorting either of the pictures, determine the dimensions needed for the pictures so the two widths add up to $630$ (they can be close but you can't be over).

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I'm not really sure if I'm supposed to be setting up a system of proportions of what not. Maybe I can set up a matrix?

Thanks for the assistance.
• Jan 27th 2009, 05:37 AM
Startbucks
Anyone have an idea?

I've played with it since.

What if I set up an augmented matrix (3x3):

So, it's something like:

605 693 546

775 546 775

But then this distorts the picture and I don't know how setting

605x + 693x_2 = 546 for example doesn't just change the height. It changes both to be that..

This can't be that hard. It's for an intro course.
• Jan 27th 2009, 07:32 AM
Startbucks
Instead of trying Lin. Alg, I was thinking of the following:

Take the 693 and subtract a certain % to get that to the right height. So,

693 - 693*21.2% = 693 - 693*.212 = 546.084 which is pretty close

So then just reduce the width by 21.2%...

605 - 605*.212 = 476.74

This will make them the same height (or very close- not sure how to get exact)

Is this right?

So for the 2nd one then do I have to find the % to make it 630 in width and then adjust the result in the first part by some % to make them fit next to each other?