Question

A floral design on a floor is made up of 16 triangular tiles, each having sides 9 cm, 28 cm and 35 cm. Find the cost of polishing the tiles at the rate of Rs 2.50 per cm².

Answer 1

Area of one triangular tile can be found in the following manner:
$$\begin{gathered} \mathrm{Let}: \\ a=9\mathrm{cm},b=28\mathrm{cm}\mathrm{and}c=35\mathrm{cm} \\ s=\frac{a+b+c}{2}=\frac{9+28+35}{2}=36\mathrm{cm} \\ \mathrm{By}\mathrm{Heron}\text{'}\mathrm{s}\mathrm{formula},\mathrm{we}\mathrm{have}: \\ \mathrm{Area}\mathrm{of}\mathrm{triangle}=\sqrt{s(s-a)(s-b)(s-c)} \\ =\sqrt{36(36-9)(36-28)(36-35)} \\ =\sqrt{36\times 27\times 8\times 1} \\ =\sqrt{9\times 4\times 3\times 9\times 4\times 2} \\ =9\times 4\sqrt{6} \\ =88.2{\mathrm{cm}}^2 \end{gathered}$$

∴ Area of 16 triangular tiles = $16\times 88.2=1411.2{\mathrm{cm}}^2$
Cost of polishing 1 cm² of area = Rs 2.5
Cost of polishing 1411.2 cm² of area = $2.5\times 1411.2=\mathrm{Rs}3528$