Question

A triangular board of perimeter 32m has two sides of equal length and third side is of length 12m.find the cost of painting it at the rate of Rs150 meter square. [given root 2= 1.41 and root 3= 1.73]

Answer 1

$$\begin{gathered} \mathrm{Let}a,b,c\mathrm{are}\mathrm{sides}\mathrm{of}△. \\ \mathrm{Now},a=x\mathrm{m} \\ b=x\mathrm{m} \\ c=12\mathrm{m} \\ \mathrm{Perimeter}=32\mathrm{m} \\ \Rightarrow a+b+c=32 \\ \Rightarrow x+x+12=32 \\ \Rightarrow 2x=20 \\ \Rightarrow x=10 \\ \mathrm{So},a=b=10\mathrm{m} \\ \mathrm{Semiperimeter},s=\frac{32}{2}=16\mathrm{m} \\ \mathrm{ar}.\mathrm{of}△=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)} \\ =\sqrt{16\times 6\times 6\times 4} \\ =4\times 6\times 2 \\ =48{\mathrm{m}}^2 \\ \mathrm{So},\mathrm{cost}\mathrm{of}\mathrm{painting}1{\mathrm{m}}^2\mathrm{area}=\mathrm{Rs}150 \\ \therefore \mathrm{cost}\mathrm{of}\mathrm{painting}48{\mathrm{m}}^2\mathrm{area}=\mathrm{Rs}150\times 48 \\ =\mathrm{Rs}7200 \end{gathered}$$