2.1+Trading+Land

KS 1/27/09 Math 8D

Problem 2.1
===Suppose you own a square piece of land with sides n meters long. You trade your land for a rectangular lot. The length of your new lot is 2 meters longer that the side length of your original lot, and the width of your new lot is 2 meters shorter than the side length of the original lot.===

A.

 * Original Square || Orignial Square || new rectangle || new rectangle || new rectangle || Difference in ||
 * Side length (m) || Area (m2) || Length (m) || Width (m) || Area (m2) || in areas (m2) ||
 * 3 || 9 || 5 || 1 || 5 || 4 ||
 * 4 || 16 || 6 || 2 || 12 || 4 ||
 * 5 || 25 || 7 || 3 || 21 || 4 ||
 * 6 || 36 || 8 || 4 || 32 || 4 ||
 * 7 || 49 || 9 || 5 || 45 || 4 ||
 * n || n2 || n+2 || n-2 || (n+2)(n-2) ||  ||

B.
For each side lengths, the area of the new lot is 4m2 smaller than the original one so it wouldnt make a fair trade.

C.
expressions shown in table.

1a.
on graph paper.

b.
A=(n+2)(n-2)

c.
The graph looks like a parabola but upside down.

d.
all values for area and side length makes sense except for negative side lengths.

2a.
for table investigation 1 and investigation 2 are not similar because investigation 1 increases and decreases but investigation 2 only increases but they are similar because they both increase at first.

b.
for grapths investigation 1 and 2 are not similar because investigation 1 is a parabola but investigation 2 it is a parabola but upside down. they are similar by having parabolas.

c.
for equations investigation 1 and 2 are similar by getting questions of an area but investigation 2 was an expression.

3.
I think the reade offered by U.S. malls Incorpreates isn't a good idea to own a private lot because it will be smaller.