anonymous
  • anonymous
The width and length of a rectangle are in the ratio of 2 to 3. If both are increased by 3 units, then the ratio is 3 to 4. The ratio of the areas of the rectangles is ___ 3 2 4 1 to___ 4 1 2 3
Mathematics
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SOLVED
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chestercat
  • chestercat
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freckles
  • freckles
well you have some equations given: \[\frac{W}{L}=\frac{2}{3} \\ \text{ and } \\ \frac{W+3}{L+3}=\frac{3}{4}\]
freckles
  • freckles
weird thing is they don't make it clear if they want you to do smaller area to bigger area or bigger area to smaller area
anonymous
  • anonymous
so its 4 to 3?

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anonymous
  • anonymous
@freckles
freckles
  • freckles
how did you get 4 to 3?
freckles
  • freckles
you know it is asking you to compute the area of a small rectangle with dimensions W and L versus finding the area of a bit larger rectangle with dimensions W+3 and L+3?
freckles
  • freckles
the area of rectangle is width * length
anonymous
  • anonymous
\[\frac{ w }{ l }=\frac{ 2 }{ 3},w=\frac{ 2 }{ 3 }l\] again \[\frac{ w+3 }{ l+3 }=\frac{ 3 }{ 4 },\frac{ \frac{ 2 }{ 3 }l+3 }{ l+3 }=\frac{ 3 }{ 4 },\frac{ 2l+9 }{ 3l+9 }=\frac{ 3 }{ 4 }\] 9l+27=8l+36 l=9 \[w=\frac{ 2 }{ 3 }*9=6\] area of smaller triangle=9*6=54 L=9+3=12 W=6+3=9 area of bigger triangle=12*9=108 ratio of areas=54/108=1/2
anonymous
  • anonymous
\[\frac{ w }{ l }=\frac{ 2 }{ 3},w=\frac{ 2 }{ 3 }l\] again \[\frac{ w+3 }{ l+3 }=\frac{ 3 }{ 4 },\frac{ \frac{ 2 }{ 3 }l+3 }{ l+3 }=\frac{ 3 }{ 4 },\frac{ 2l+9 }{ 3l+9 }=\frac{ 3 }{ 4 }\] 9l+27=8l+36 l=9 \[w=\frac{ 2 }{ 3 }*9=6\] area of smaller triangle=9*6=54 L=9+3=12 W=6+3=9 area of bigger triangle=12*9=108 ratio of areas=54/108=1/2

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