Question

floral design on a floor is a made up of 16 tiles that are triangular side of a triangle Being 9 cm,28 cm and35 cm . Find the cost of polishing the tiles at the rate of 50 p per cm².​

Answer 1

$\huge{\underline{\underline{\sf{\purple{Required\:Answer:}}}}}$

For one tile

⠀⠀⠀⠀α = 9 cm, b = 28 cm, c = 35 cm

$\displaystyle{\sf{ \therefore \:\:\:\:\:s= \dfrac{a+b+c}{2} = \dfrac{9+28+35}{2}}}$

$\implies{\sf{36\:cm}}$

$\therefore$ Areα of one tile

$\displaystyle{\sf{= \sqrt{s(s-a)(s-b)(s-c)}}}$

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

$\displaystyle{\sf{= \sqrt{36(17)(8)(1)}}}$

$\displaystyle{\sf{=36\sqrt{6}cm^{2}}}$

${\therefore}$ Areα of 16 tile

$\displaystyle{\sf{=36\sqrt{6}cm^{2}\times16 = 576\sqrt{6}cm^{2}}}$

${\therefore \:\:\:\:}$ Cost of polishing the tiles αt the rαte of 50 p per cm² .

:$\implies{\sf{576 \sqrt{6} \times 50p = ₹ \dfrac{576 \sqrt{6} \times 60}{100}}}$

:$\implies{\sf{₹288 \sqrt{6}}}$

$\large{\implies{\boxed{\bf{\pink{₹705.60}}}}}$

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$\huge{\underbrace{\sf{\blue{Explore\:More!}}}}$

Areα of α Triαngle — By Heron's Formulα

Areα of α triangle =

$\displaystyle{\boxed{\sf{\orange{ \sqrt{s(s-a)(s-b)(s-c)}}}}}$

• Where α, b and c αre the sides of the triαngle, αnd s = semi - perimeter, i.e., hαlf the perimeter of the triαngle = $\displaystyle{\boxed{\sf{\red{ \dfrac{a+b+c}{2}}}}}$

This formulα for the areα of α triαngle wαs given by Her on and is therefore known as Heron's Formulα.

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Answer 2

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Question :

Flora design on a floor is a made up of 16 tiles that are triangular side of a triangle being 9cm, 28cm and 35cm. Find the cost of polishing the tiles at the rate of 50 p per cm².

Given:

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

$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

$\\ \implies \large \sf \: semi \: perimeter \: of \: tile \: = \frac{a + b + c}{2}$

$\\ \\ \implies \large \sf \: semi \: perimeter \: of \: tile \: = \frac{35 + 28 + 9}{2} = 36cm$

$\\ \\ \implies \boxed{\large \sf \: \: semi \: perimeter \: of \: tile \: = 36cm}$

$\\ \\ \implies \large \sf \: area \: of \: \triangle = \sqrt{s(s - a )(s - b)(s - c)}$

$\\ \\ \implies \large \sf \: area \: of \: \triangle = \sqrt{36(36 - 35)(36 - 28)(36 - 9)}$

$\\ \\ \implies \large \sf \ area \: \: of \: \: \triangle = \sqrt{36 \times 1 \times 8 \times 27}$

$\\ \\ \implies \large \sf \: area \: of \: \triangle = 36 \times 2.45$

$\\ \\ \implies \boxed{ \large \sf \: area \: of \: \triangle \: = 88.2 {cm}^{2} }$

$\\ \\ \implies \large \sf \: area \: of \: total \: 16 \: tiles \: = 16 \times 88.2 = 1411.2 {cm}^{2}$

$\\ \\ \implies \boxed {\large \sf{area \: of \: total \: 16 \: tiles \: = 1411.2 {cm}^{2} }}$

$\\ \\ \implies \large \sf \: cost \: of \: polishing \: per \: {cm}^{2} \: area \: = 50p$

$\\ \\ \implies \large \sf{ \: cost \: of \: polishing \: 1411.2 {cm}^{2} \: area \: = 50 \times 1411.2}$

$\\ \\ \implies\large{\boxed{\sf{ cost \: of \: polishing \: 1411.2cm^2 \: area=Rs 705.60}}}$