Question

The sides o9f triangular field are 41m 40m and 9m. find the number of rose beds that can be prepared in the field if each rose bed on an average needs 900cm2 space

Answer 1

$\huge\bf\red{\underline{\underline{Given}}}\::$

• $\sf\gray{The \:sides\:of\: triangular\: field\: are \:41m,\:40m \:and \:9m.}$

$\huge\bf\red{\underline{\underline{To\:Find}}}\::$

• $\sf\gray{No.\:of\:rose\:beds\:that \:can\: be\: prepared\:in\: the \:field \:if \:each\: rose\: bed \:on \:an \:average \:needs\: 900cm^{2}\: space.}$

$\huge\bf\red{\underline{\underline{Solution}}}\::$

$\blacklozenge\:{\underline{\boxed{\sf{\orange{\:Area_{\:triangle}\:=\:\sqrt{s(s-a)(s-b)(s-c)}\: }}}}}$

$\to\:\sf\purple{S\:=\:\dfrac{41\:+\:40\:+\:9}{2}}$

$\to\:\sf\green{S\:=\:45m}$

$\to\:\sf\purple{Area\:=\:\sqrt{45\:(4)\:(5)\:(36)}}$

$\to\:\sf\green{Area\:=\:\sqrt{32400}}$

$\to\:\sf\purple{Area\:=\:180m^{2}}$

$\star\:\sf\underline\red{Converting\:into\: centimetre}$

$\mapsto\:\sf\orange{1800000cm^{2}}$

$\clubsuit\:{\boxed{\sf{\blue{\:No.\:of\:rose\:beds\:=\:\dfrac{Total\:area}{Area\: occupied\:by\:1\:rose\:bed}\:}}}}$

$\hookrightarrow\:\sf\purple{No\:of\:rose\:beds\:=\:\dfrac{\cancel{1800000}^{^{^{{\tiny{2000}}}}}}{\cancel{900}_{_{_{1}}}}}$

$\hookrightarrow\:{\underline{\boxed{\tt{\pink{\:No\:of\:rose\:beds\:=\:2000\:}}}}}$