Question

ABCD is a rectangle it's adjacent sides are in the ratio 3:5 and it's perimeter is 48cm find the length of the side

Answer 1

ABCD is a rectangle, its adjacent sides are in the ratio of 3 : 5 and its perimeter is 48 cm.

To find : the length of the sides of rectangle.

solution : as it is given that adjacent sides are in the ratio of 3 : 5.

let proportionality constant is k.

width of rectangle, b = 3k

length of rectangle, l = 5k

now perimeter of rectangle = 2 (l + b)

⇒48 cm = 2 (3k + 5k)

⇒24cm = 8k

⇒k = 24/8 = 3

now length of rectangle = 5k = 5 × 3 = 15cm

and width of rectangle = 3k = 3 × 3 = 9 cm

Answer 2

$\bf{\underline{\underline{\bigstar\bigstar\: Figure : }}}$

$\:\:$

$\setlength{\unitlength}{1.6mm}\begin{picture}(5,6)\put(0,25){\line(1,0){35}}\put(0,0){\line(1,0){35}}\put(0,0){\line(0,1){25}}\put(35,0){\line(0,1){25}}\put(17,-2){5x}\put(18,-2){}\put(35,15){3x}\put(18,0){ }\end{picture}$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\:Given : }}}$

$\:\:$

• $\footnotesize{ Ratio \: of \: adjacent \: side = 3 : 5 }$

• $\textfootnotesize{ Perimeter = 48cm }$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\: To \: Find : }}}$

$\:\:$

• $\textfootnotesize{ Length \: of \: rectangle }$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\: Solution :}}}$

$\:\:$

$\bold{\footnotesize{ Let, \: the \: multiple \: of \:ratio \: be \: x = 3 : 5 }}$

$\:\:$

$\textfootnotesize{ Perimeter \: of \: rectangle = 2( l + b )}$

$\textfootnotesize{\implies 48cm = 2( 3x + 5x )}$

$\textfootnotesize{\implies 48cm = 2 \times 8x }$

$\textfootnotesize{\implies 48cm = 16x }$

$\textfootnotesize{\implies \dfrac{48cm}{16} = x }$

$\textfootnotesize{\implies \cancel{\dfrac{48cm}{16}} = x }$

$\textfootnotesize{\implies 3cm = x }$

$\:\:$

$\rule{200}3$

$\:\:$

$\textfootnotesize{ Length \: of \: rectangle = 3x }$

$\textfootnotesize{\implies Length \: of \: rectangle = 3 \times 3cm }$

$\textfootnotesize{\implies Length \: of \: rectangle = 9cm }$