Question

$\underline{\bf{Question}}$ :-
A floral design on a floor is a made up of 16 tiles which are triangular, the sides of the triangle begin 9 cm, 20 cm and 35 cm find the cost of polishing the tiles at the rate of 50p per cm².

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Answer 1

$\huge\tt{\bold{\purple{\underbrace{\red{\mathfrak{ɾҽզմíɾҽժ ⠀αղsաҽɾ♡༄}}}}}}$

$\huge{\fbox{\pink{Given:-}}}$

Side number one (a) = 9 cm.

Side number two (b) = 28 cm.

Side number three (c) = 35 cm.

The rate of polishing = 50p per cm².

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$\huge{\fbox{\pink{To find:-}}}$

The cost of polishing the tiles.

⠀

$\huge{\fbox{\pink{Solution:-}}}$

Area of tiles = 16 x area of 1 ∆

$\huge{\green{Semiperimeter}} \\ \\ s = semiperimeter \: of \: the \: triangle \\ \\ s = \frac{a + b + c}{2} \\ \\ \implies \: s = \frac{9 + 28 + 35}{2} \\ \\ \implies \: s = \frac{72}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \: s = 36 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\huge{\green{area \: of \: one \: triangle}} \\ \\ area \: of \: one \: triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \: area \: of \: one \: triangle = \sqrt{36(36 - 9)(36 - 28)(36 - 35)} \ \\ \implies \: area \: of \: one \: triangle = \sqrt{36 \times 7 \times 8 \times 1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \: area \: of \: one \: triangle = \: 36 \sqrt{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\huge{\green{area \: of \: tiles}} \\ \\ area \: of \: tiles = 16 \times 36 \sqrt{6} \\ \implies \: area \: of \: tiles = 1410.20 \: {cm}^{2}$

$\huge{\green{cost \: of \: polishing}} \\ \\ cost \: of \: polishing \: per \: {cm}^{2} = 50p \\ \implies \: cost \: of \: polishing \: per \: {cm}^{2} = \frac{1}{2} rupee \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies cost \: of \: polishing \: 1410.90 \: {cm}^{2} = 1410.90 \times \frac{1}{2} \\ \implies cost \: of \: polishing \: 1410.90 \: {cm}^{2} = 705.45 \: rupee$

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Answer 2

Answer:

$\large{ \pink{ \rm{ \underline{given : - }}}}$

sides of the triangular tile are$\bold{ {9cm ,\: 20cm \: and \: 35cm}}$

$\large \rm{ \pink{ \underline{to \: find : - }}}$

Cost of polishing the tiles at the rate of 50p per$\rm {cm}^{2}$

$\large{ \pink{ \rm{ \underline{solution : - }}}}$

Let the sides of the be$\bold{a, \: b, \: and \: c}$

$\rm{a = 9cm \: b = 28cm \: c = 35cm}$

semiperimeter of triangle$\rm{s = \frac{a + b + c}{2} }$

$\rm{s = \frac{9cm + 28cm + 35cm}{2} }$

$\rm{s = \frac{ \cancel{72cm}}{ \cancel2 } } = 36cm$

$\rm{area \: of \: 1 \triangle = \sqrt{s( s-a )( s-b )(s - c)} }$

$\rm{ = \sqrt{36(36 -9 )(36 -28 ) (36 -35 )} }$

$= \sqrt{36 \times 27 \times 8 \times 1}$

=$\sqrt{2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 2 \times 2 \times 2 \times 1}$

$= 2 \times 2 \times 3 \times 3 \sqrt{2 \times 3 }$

$=36 \sqrt{6}$

$= \rm{88.2 {cm}^{2} }$

$\rm{area \: of \: 16 \triangle = 88.2 \times 16}$

$\rm{ = 1411.2 {cm}^{2} }$

Cost of polishing 1 cm^2 =50p

Cost of polishing$\rm{ {1411.2cm}^{2} }$=

$1411.2 \times \frac{50}{100}$

$= \frac{702720}{1000}$

$\huge \red{= 702.720}$