Question

the area and length of one diagonal of a rhombus are given as 200 CM square and 10 cm respectively the length of other diagonal is​

Answer 1

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

$\tt The \:area\: and\: length\: of \:one\: diagonal\: of \:a \:rhombus\\\tt are\: given \:as \:200\: cm\: square\: and\: 10 \:cm\:respectively\\\tt the \:length \:of\: other\: diagonal \:is$

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

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

• $\sf\bf Area\:of\:Rhombus(A) = 200 \:cm$
• $\sf \bf Length \:of \:first \:diagonal (d_1) = 10\:cm$

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

• $\sf \bf Length \:of \:second\:diagonal (d_1)$

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

${\color {red} \underline {\sf Let\:the\:second \:diagonal \:be=x}}$

${\boxed {\boxed {\color{blue} {\sf \bf A=\dfrac{d_1 \times d_2}{2}}}}}$

• $\sf A=area \:of \:Rhombus$
• $\sf d_1=first \:diagonal$
• $\sf d_2=second\:diagonal$

${\underbrace {\overbrace {\color{orange} {\sf Substitute\: the\: values}}}}$

$\sf \bf \implies 200=\dfrac{10\times x}{2}$

$\sf \bf \implies 200\times 2=10x$

$\sf \bf \implies 400=10x$

$\sf \bf \implies x=\dfrac{400}{10}$

$\sf \bf \implies x=\dfrac{40\cancel {0}}{1\cancel {0}}$

$\implies {\boxed {\color {green} {\sf \bf x=40\:cm}}}$

${\color {purple} \underline {\tt \therefore The\:length \:of \:second\:diagonal \:is \:40\:cm}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

___________________________________________

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

$\sf Area \:of \:rhombus =\dfrac{d_1\times d_2}{2}$

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

$\sf Area \:of \:triangle =\dfrac{1}{2}bh$