Question

3) The measurements of the perimeter and breadth of a rectangle are 138m and 24m. Find the
corresponding length of rectangle.​

Answer 1

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt 3) \:The\: measurements\: of\: the\: perimeter\: and\: breadth \\\tt of \:a \:rectangle \:are \:138\:m\: and\: 24\:m. \:Find \:the\\\tt corresponding \:length\: of\: rectangle.$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\bf Perimeter \:of\:the \:rectangle =138\:m$
• $\bf Breadth \:of\:the \:rectangle =24\:m$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\bf Length \:of \:the \:rectangle$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\pink {\underline {\pmb {\bf {Length \:of \:the \:rectangle}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {P=2\big(l+b\big)}}}}}}}$

• $\sf P= perimeter \:of\:the \:rectangle$
• $\sf l= length \:of\:the \:rectangle$
• $\sf b= breadth \:of\:the \:rectangle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies 138=2\Big(l+24\Big)$

$\bf \implies 138=2l+48$

$\bf \implies 2l=138-48$

$\bf \implies 2l=90$

$\bf \implies l=\dfrac{90}{2}$

$\bf \implies l=\dfrac{\cancel{90}}{\cancel{2}}$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {l=45\:m}}}}}}$

${\underbrace {\red {\underline {\red {\overline {\sf {\pmb {{\therefore} The\:length\:of \:the \:rectangle \:is\:45\:m}}}}}}}}$

___________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf Area \:of \:the \:rectangle =l\times b$

$\sf Perimeter\:of \:the \:rectangle =2(l+b)$

$\sf Diagonal \:of \:the \:rectangle =\sqrt{{l}^{2}+{b}^{2}}$