Question

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

Answer 1

well you have some equations given:
\[\frac{W}{L}=\frac{2}{3} \\ \text{ and } \\ \frac{W+3}{L+3}=\frac{3}{4}\]

Answer 2

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

Answer 3

so its 4 to 3?

Answer 4

@freckles

Answer 5

how did you get 4 to 3?

Answer 6

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?

Answer 7

the area of rectangle is width * length

Answer 8

\[\frac{ w }{ l }=\frac{ 2 }{ 3},w=\frac{ 2 }{ 3 }l\]
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

Answer 9

\[\frac{ w }{ l }=\frac{ 2 }{ 3},w=\frac{ 2 }{ 3 }l\]
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