Question

The length of a hall is 20 m and width 16 m.The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the
four walls. Find the height of the hall.​

Answer 1

Step-by-step explanation:

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Answer 2

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

$\tt The\: length\: of \:a\: hall \:is \:20\: m \:and\: width\: 16\:m.\\\tt The \:sum\: of\: the\: areas\: of\: the\: floor\: and\: the\\\tt flat\: roof\: is \:equal\: to\: the\: sum\: of \:the \:areas\:of \\\tt the\: four\: walls.\: Find\: the \:height\: of \:the\: hall.$

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

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

• $\sf \bf Length =20\:m$
• $\sf \bf Width=16\:m$
• $\sf \bf (area\:of\:4\:walls)=(area\:of\:floor) +(area\:of\:flat\:roof)$

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

• $\sf \bf Area\:of\:floor$
• $\sf \bf Area\:of \:flat\: roof$
• $\sf \bf Area\:of\:4\:walls$
• $\sf \bf Height\:of\:the\:hall$

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

${\boxed {\boxed {\color {blue} {\sf \bf A= l \times b}}}}$

• $\sf \bf A=area\:of\:rectangle$
• $\sf \bf l=length$
• $\sf \bf b=breadth$

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

$\tt {\color{purple} {Area\:of\:floor=A_1}}$

$\sf \bf \implies A_1=20 \times 16$

$\implies{\boxed {\color {red}{\sf \bf A_1=320\:{m}^{2}}}}$

$\tt {\color{purple} {Area\:of\:floor=A_2}}$

$\sf \bf \implies A_2=20 \times 16$

$\implies{\boxed {\color {red}{\sf \bf A_2=320\:{m}^{2}}}}$

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${\boxed {\boxed {\color {blue} {\sf \bf L.S.A=2h( l +b) }}}}$

• $\sf \bf L.S.A=area \:of\:4\:walls$
• $\sf \bf h=height$
• $\sf \bf l=length$
• $\sf \bf b=breadth$

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

$\tt {\color{purple} {Area\:of\:4\:walls=A_3}}$

$\sf \bf \implies A_3= 2h(20+16)$

$\sf \bf \implies A_3= 2h(36)$

$\implies{\boxed {\color {red}{\sf \bf A_3=72h\:{m}^{2}}}}$

------------------------------------------------------------

${\boxed {\color {purple} {\sf \bf (area\:of\:4\:walls)=(area\:of\:floor) +(area\:of\:flat\:roof)}}}$

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

$\sf \bf \implies A_3=A_1+A_2$

$\sf \bf \implies 72h=320+320$

$\sf \bf \implies 72h=640$

$\sf \bf \implies h=\dfrac{640}{72}$

$\implies {\boxed {\boxed{\color {green} {\sf \bf h=8.8888888888888 \:\:\:or\:\:\:h \approx 8.89}}}}$

$\tt\underline {\color{orange} {\therefore The\:height \:of\:the\:wall\:is\:h=8.8888888888888 \:or\:h \approx 8.89}}$

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

__________________________________________

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

$\sf \bf L.S.A\:of\:cuboid =2h(l+b)$

$\sf \bf T.S.A\:of\:cuboid =2(lb+bh+hl)$

$\sf \bf Volume\:of\:cuboid =l \times b \times h$

${\mathbb{\colorbox {orange} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {lime} {\boxed{\boxed{\boxed{\boxed{\boxed{\colorbox {aqua} {@suraj5070}}}}}}}}}}}}}}}$