Question

The given figure shows a small garden . The shaded area is reserved for planting flowers and the rest of the area is for grass, Find the ratio of the area of the garden reserved for planting flowers to the area reserved for grass.

Answer 1

Hint: For finding the ratio of area first find the numeric value of the area reserved for grass and area reserved for flowers . After finding the areas represent them into the fraction and simplify then finally convert to ratio.

Formula used:
area of the rectangle = length times breadth=\[l \times b\]

Complete step-by-step answer:
Length of the garden \[l\]= 12\[m\] Breadth of the garden \[b\]= 5 \[m\]
Area of the garden =\[l \times b\]=\[12 \times 5 = 60{m^2}\]
Length of the shaded area = length of the garden – length of unshaded part = ( 12-4 )\[m\]=8\[m\]
Breadth of the shaded area = 3\[m\]
Shaded area reserved for flowers =\[l \times b\]= \[8 \times 3 = 24{m^2}\]
Area reserved for grass = Area of garden – area reserved for flowers
 Area reserved for grass = \[60 - 24 = 36{m^2}\]
Ratio of the area of the garden reserved for planting flowers flowers to the area reserved for grass
\[\dfrac{{24}}{{36}} = \dfrac{2}{3} \Rightarrow 2:3\]

Hence the ratio is \[2:3\].

Note: In the problems of ratios remember a ratio between two or more quantities is a way of measuring their value compared to each other.
The ratio 4:2 is the same as the 8:4. They are just two ways of writing the same thing. Just like there are different ways of writing a fraction , there are many ways to write a ratio too. In writing the ratio the first term is called antecedent and the second term is called consequent.