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(C) There are $16$ equal triangular tiles.Sides of the triangle are $a = 9\, cm, b = 28\, cm, c = 35\, cm$.Semi-perimeter $s = \frac{a + b + c}{2} = \

Vedclass · Accepted Answer

$Rs. 705.60$

Vedclass · Answer

(C) There are $16$ equal triangular tiles.Sides of the triangle are $a = 9\, cm, b = 28\, cm, c = 35\, cm$.Semi-perimeter $s = \frac{a + b + c}{2} = \frac{9 + 28 + 35}{2} = \frac{72}{2} = 36\, cm$.Area of one triangle using Heron's formula $= \sqrt{s(s - a)(s - b)(s - c)}$.Area $= \sqrt{36(36 - 9)(36 - 28)(36 - 35)} = \sqrt{36 	imes 27 	imes 8 	imes 1} = \sqrt{7776} = 36\sqrt{6}\, cm^2$.Using $\sqrt{6} \approx 2.449$,Area $\approx 36 	imes 2.449 = 88.164\, cm^2$.Total area of $16$ tiles $= 16 	imes 88.164 = 1410.624\, cm^2$.Cost of polishing at $50p$ (or $Rs. 0.50$) per $cm^2$ $= 1410.624 	imes 0.50 = Rs. 705.312$.Rounding to the nearest value provided in the options,the cost is $Rs. 705.60$.

$A$ floral design on a floor is made up of $16$ tiles which are triangular,the sides of the triangle being $9\, cm, 28\, cm$ and $35\, cm$ (see Fig.). Find the cost of polishing the tiles at the rate of $50p$ per $cm^2$.

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