Math Help #2

Test Preparation
1

<p>I have a new set a math questions that I am stumped on. I have been looking at them for a while and cant seem to get one. Someone, please help. Anyone! These questions have to do with Products and Factoring of Polynomials. </p>

<li><p>When .5cm was planed off each of the six faces of a wooden cube, its volume decreased by 169cm^3 (cubed). Find its new volume. </p></li>
<li><p>A farmer plans to use 21m of fencing to enclose a rectangular pen having area 55m^2 (squared). Only three sides of the pen need fencing because part of an existing wall will form the fourth side. Find the dimensions of the pen.</p></li>
<li><p>The width. length, and diagonal of a rectangle are consecutive even integers. Find the integers.</p></li>
<li><p>Give a convincing argument why the width, length, and diagonal of a rectangle cannot be consecutive odd integers.</p></li>
<li><p>A recntagular corner lot, orginally twice as long as it is wide, lost a 2 meter strip along two adjacent sides to to street widening. Its new area is 684m ^2 (squared). Find the new dimensions.</p></li>
</ol>

<p>Please include an explanation too. Thanks guys, you really help me a lot!</p>

2

<p>I'm lazy so I will only answer the easiest/quickest one.</p>

<ol>
<li> 6 width, 8 length, 10 diagonal</li>
</ol>

<p>This comes from the 3,4,5 triangle. You simply mulitply each value by 2.</p>

3

<p>First one is 343.</p>

4

<ol>
<li><ol>
<li>Set up an equation: x^3 - (x-1)^3 = 169. Solve for x. Subtract 1 from<br>
x and cube that answer. This is the new volume.</li>
</ol></li>
<li><p>5m X 5m. 5 + 5 + 11 = 21 and 5 X 11 = 55.</p></li>
<li><p>See Flipsta's post.</p></li>
<li><p>According to Pythagorean theorem, a^2 + b^2 = c^2. Assume a and b are<br>
odd. An odd number multiplied by an odd number always yields an even<br>
number. So a^2 and b^2 will both be odd numbers. An odd number plus an<br>
odd number is always even. So, c^2 must be even if a and b are odd
integers. The square roor of an even integer cannot be odd. </p></li>
<li><p>18m X 38m. Set up an equation: (w-2)(2w-2) = 684 meters squared.</p></li>
</ol>

5

<p>I meant 5m X 11m for #2.</p>