Question 1041248
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I need help on these three questions:
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2a = 3b
a^2 + b^2 = 117
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Find two numbers with a sum of 6 and with a quotient of -4.
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A twenty-six meters of fencing is used to enclose a rectangular lot with an area of 42 square meters. What are the dimensions of the lot?

I want to learn more about Quadratic Equations so I had these examples from the book. Please help for a test tomorrow!
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<pre>
1.  2a = 3b,              (1)
    {{{a^2 + b^2}}} = 117.        (2)

    Multiply the eqn.(2) by 4 (both sides). You will get 

    {{{4a^2 + 4b^2}}} = 4*117,   or

    {{{(2a)^2 + 4b^2}}} = 468.    (3)

    Now replace 2a in (3) by 3b, according to (1). You will get

    {{{(3b)^2 + 4b^2}}} = 468,   or  {{{9b^2 + 4b^2}}} = 468,   or   {{{13b^2}}} = 468.

    Now divide both sides by 13. You will get

    {{{b^2}}} = {{{468/13}}} = 36.

    Hence, b = +/-{{{sqrt(36)}}} = +/-6.

<U>Answer</U>.  b = 6,  a = 9   and/or   b = -6, a = -9.
</pre>

Regarding your question  #3, see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Problems-on-the-area-and-the-perimeter-of-a-rectangle.lesson>Problems on the area and the dimensions of a rectangle</A>

in this site.


You will find there a lot of solved problems similar to yours.
Read them and consider them as the samples.
Then solve your problem on your own.


Also, look into this file &nbsp;<A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


It is your free online textbook in ALGEBRA-I.