# Math

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a rectangle is 3 times as wide as a square. the rectangle's length is 15 ft shorter than 5 times the square's length. Given that the sum of the two perimeters must be less than 150 ft, find the set of all possible lengths for the rectangle

• Math -

I see from the first statement that since the rectangle length is 15ft less than five times the sqare side, the square side cannot be less than 3.

lets make it 3.01 for the square. Now, the width of the rectangle then will be 3.01x3, or 9.03 width, and length .05.

So that is the smallest rectangle and the smallest square.

Now the largest: Perimerter sum <150

150>4s+2w+2l
150>4s+2*3s + 2*(15-5s)
solve for s, then w, then l.

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