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 __ to __ .

Answer 1

hi

Answer 2

we can use fractions to solve this. put the width as \(w\) and the length as \(l\) so we know
\[\frac{w}{l}=\frac{2}{3}\implies 3w=2l\implies l=\frac{3}{2}w \] now if we increase them both by 3 we know
\[\frac{w+3}{l+3}=\frac{3}{4}\implies 4(w+3)=3(l+3)\]
\[4w+12=3l+9\] now we can replace \(l\) by \(\frac{3}{2}w\) and solve
\[4w+12=3\times \frac{3}{2}w+9\] for \(w\)

Answer 3

before increase
let width=2x length=3x
after increase
you can get width =2x+3 length=3x=3
but width/length=3/4
so (2x+3)/(3x+3)=3/4
x=3
then the ratio of areas((2x)*(3x))/((2x+3)*(3x+3))=1:2