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I have a algebra homework question i cant figure out.

a square and rectangle both with equal area. one side of the rectangle is 3 ft shorter than the square and the other side is 4 ft longer than the square. find the length of one side of the rectangle

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2 Answers

When in doubt, draw it out. When you can see the square drawn next to the rectangle and you fill in all variables that you know, you will often be able to figure out what the next logical step would be in solving. The same equation for solving this problem may not work with different shapes or other problems so it is good to fall back on your own ability problem solve. You never know what will click in your head when you see the pictures and start filling them in like a puzzle, the picture just might shine through.

Let x = the length of the square.

The dimension of the rectangle is x+4 by x-3.

Since the two areas are equal,

(x+4)(x-3) = x^2

Expand and simplify,

x = 12

x-3 = 9

x+4 = 16

Answer: The length of the the rectangle is 16 ft, and the width is 9 ft.