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gizmo_the_mogwai [7]
3 years ago
13

If you have 24 square pieces of wood, describe all

Mathematics
1 answer:
nika2105 [10]3 years ago
6 0

Answer:  11 (or 10 if the square is not to be counted)

<u>Step-by-step explanation:</u>

Start with 1: If you have 1 piece on the top <em>and 1 piece on the bottom</em>, then there are 24 - 2 = 22 pieces left for the sides, which results in 11 on each side.  Continue this with 2 pieces on the top, then 3 pieces on the top, etc.  You will eventually see a pattern.

Here are all of the ways you can lay out the pieces of wood to form 4 sides:

1 x 11

2 x 10

3 x 9

4 x 8

5 x 7

6 x 6  --> this is a square.  should this be counted as a rectangle?

7 x 5

8 x 4

9 x 3

10 x 2

11 x 1

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Jacob wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn,so he needs no fence on that side.

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Now we find out x coordinate of vertex to find the width that maximize the area

W = \frac{-b}{2a}

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W = \frac{-(400)}{2(-2)}=100

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A(W) = -2(100)^2 + 400(100)= 20000

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