Question 283963
<pre><font size = 4 color = "indigo"><b>
{{{drawing(300,300,-1,16,-1,16,triangle(0,0,14.93948574,10.04050625,0,10.04050625),
triangle(0,0,14.93948574,10.04050625, 14.93948574),
locate(15.2,5,y), locate(7.5,0,x), locate(7.5,5.2,18) 


 )}}}

The diagonal, which is 18 inches is the hypotenuse of
the right triangle with legs x and y. Using the
Pythagorean theorem, we have the equation:

{{{x^2+y^2=18^2}}}
{{{x^2+y^2=324}}} 

The area of the whole rectangle given as 150 square inches 
is the length x times the width y.  So we have the 
equation:

{{{xy=150}}}

So we have the system:

{{{system(x^2+y^2=324,xy=150)}}}

Solve the second equation for y

{{{xy=150}}}
{{{y=150/x}}}

Now we substitute {{{150/x}}} for {{{y}}} in the
equation:

{{{x^2+y^2=324}}}
{{{x^2+(150/x)^2=324}}}
{{{x^2+150^2/x^2=324}}}
{{{x^2+22500/x^2=324}}}

Multiply through by {{{x^2}}} to clear of fractions:

{{{x^4+22500=324x^2}}}

Get 0 on the right by subtracting {{{324x^2}}} from
both sides:

{{{x^4+22500-324x^2=0}}}

Get it in descending order:

{{{x^4-324x^2+22500=0}}}

That is choice (C).

Edwin</pre>