Question

a) If $A:B=3:5$ and $B:C=4:3$, find $A:B:C$
b) Find the mean proportional to $12$ and $3$
c) The ratio between length and breath of a rectangular field is $7:5$. If the width of the sheet is $35$ m, find the length.

Answer 1

(a) $\frac{A}{B}=\frac{3}{5}=\frac{3\times 4}{5\times 4}=\frac{12}{20}$

$\frac{B}{C}=\frac{4}{3}=\frac{4\times 5}{3\times 5}=\frac{20}{15}$

Therefore, $A:B:C=12:20:15$

(b) Let the mean proportional be $x$

Then $12:x::x:3$

$\Rightarrow \frac{12}{x}=\frac{x}{3}$

$\Rightarrow x^2=36$

$\Rightarrow x=6$

(c) Let the length and breadth of the rectangle be $7x$ and $5x$

Then $5x=35$

$\Rightarrow x=7$

So. Length of the rectangle $=7x$ $=$ $7\times 7$$=49$ $m$