Find the following ratios :
The lengths of sides of a rectangle are 5 cm and 3.5 cm. Find the ratio of numbers denoting its perimeter to area.
Answer
Length of rectangle $=( l )=5 cm$,
Breadth of rectangle $=(b)=3.5 cm$
Perimeter of the rectangle $=2(l+b)$
$=2(5+3.5)$
$=2 \times 8.5$
$=17 cm$
Area of the rectangle $= Ixb$
$=5 \times 3.5$
$=17.5 cm^2$
Ratio of numbers denoting perimeter to the area of rectangle
$\begin{aligned}
& =\frac{\text { perimeter }}{\text { area }} \\
& =\frac{17}{17.5} \\
& =\frac{17 \times 10}{17.5 \times 10} \\
& =\frac{170}{175} \\
& =\frac{5 \times 34}{5 \times 35} \\
& =\frac{34}{35} \\
& =34: 35
\end{aligned}$
$\therefore$ Ratio of numbers denoting perimeter to the area of rectangle is $34: 35$.
Find the following ratios : The ratio of diagonal of a square to its side, if the length of side is 7 cm.
Answer
Length of side of square = 7 cm
$\therefore$ Diagonal of square $= \sqrt{2} \times$ side
$= \sqrt{2} \times 7$
$= 7 \sqrt{2} cm$
Ratio of diagonal of a square to its side
$=\frac{\text { diagonal }}{\text { side }}$
$=\frac{7 \sqrt{2}}{7}$
$=\frac{\sqrt{2}}{1}$
$=\sqrt{2}: 1$
$\therefore$ The ratio of diagonal of a square to its side is $\sqrt{2} : 1$.
Find the following ratios $:$ The ratio of circumference of circle with radius $r$ to its area.
Answer
Let the radius of the circle is $r.$
$\therefore$ circumference $= 2\pi r$ and area $= \pi r^2$
Ratio of circumference to the area of circle
$=\frac{\text { circumference }}{\text { area }}$
$=\frac{2 \pi r }{\pi r ^2}$
$=\frac{2}{ r }$
$=2: r$
$\therefore$ The ratio of circumference of circle with radius $r$ to its area is $2: r$.
Find the following ratios $:$ The ratio of radius to circumference of the circle.
Answer
Let the radius of circle be $r.$
then, its circumference $= 2\pi r$
Ratio of radius to circumference of the circle
$=\frac{\text { radius }}{\text { circumference }}$
$=\frac{ r }{2 \pi r }$
$=\frac{1}{2 \pi}$
$=1: 2 \pi$
The ratio of radius to circumference of the circle is $1: 2 \pi$.