Difference between revisions of "1989 AHSME Problems/Problem 6"

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==Solution==
 
==Solution==
Setting <math>y=0</math> we have that the <math>x-</math>intercept of the line is <math>x= \frac{6}{a} </math>. Similarly setting <math>x=0</math> we find the <math>y-</math>intercept to be <math>y= \frac{6}{b} </math>. Then <math> \frac{18}{ab}=\frac{1}{2}\frac{6}{a}\frac{6}{b}</math> so that <math> \frac{18}{ab} = 6</math>, simplifying we would get <math>ab=3</math>. Hence the answer is <math>\fbox{A}</math>.
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Setting <math>y=0</math> we have that the <math>x-</math>intercept of the line is <math>x= \frac{6}{a} </math>. Similarly setting <math>x=0</math> we find the <math>y-</math>intercept to be <math>y= \frac{6}{b} </math>. Then <math> \frac{18}{ab}=\frac{1}{2}\cdot\frac{6}{a}\cdot\frac{6}{b}</math> so that <math> \frac{18}{ab} = 6</math>, simplifying we would get <math>ab=3</math>. Hence the answer is <math>\fbox{A}</math>.
  
-LATEX Kevinliu08
+
-<math>LATEX</math> by Kevinliu08
  
 
== See also ==
 
== See also ==

Revision as of 02:18, 8 November 2022

Problem

If $a,b>0$ and the triangle in the first quadrant bounded by the co-ordinate axes and the graph of $ax+by=6$ has area 6, then $ab=$

$\mathrm{(A) \ 3 } \qquad \mathrm{(B) \ 6 } \qquad \mathrm{(C) \ 12 } \qquad \mathrm{(D) \ 108 } \qquad \mathrm{(E) \ 432 }$

Solution

Setting $y=0$ we have that the $x-$intercept of the line is $x= \frac{6}{a}$. Similarly setting $x=0$ we find the $y-$intercept to be $y= \frac{6}{b}$. Then $\frac{18}{ab}=\frac{1}{2}\cdot\frac{6}{a}\cdot\frac{6}{b}$ so that $\frac{18}{ab} = 6$, simplifying we would get $ab=3$. Hence the answer is $\fbox{A}$.

-$LATEX$ by Kevinliu08

See also

1989 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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