Question

The area of a triangle varies as its base and height. The area of a triangle having base 6 cm. and height 4 cm is 12sq.cm. Find the height of the triangle whose base is 8 cm and area is 36 sq.cm

Answer 1

$$\begin{gathered} \mathrm{Let}A\mathrm{denote}\mathrm{the}\mathrm{area}\mathrm{of}the\mathrm{triangle},b\mathrm{denote}\mathrm{the}\mathrm{base}\mathrm{of}the\mathrm{triangle}\mathrm{and}h \\ \mathrm{denote}\mathrm{the}\mathrm{height}\mathrm{of}the\mathrm{triangle}. \\ Thus,wehave: \\ A\alpha bh \\ \Rightarrow A=k\left(bh\right)\left(k\mathrm{is}a\mathrm{constant}.\right) \\ Now, \\ \mathrm{When}A=12\mathrm{sq}\mathrm{cm},b=6\mathrm{cm}\mathrm{and}h=4\mathrm{cm}: \\ 12=k\times 6\times 4 \\ \Rightarrow k=\frac{12}{6\times 4} \\ \Rightarrow k=\frac{1}{2} \\ Thusthee\mathrm{quation}\mathrm{of}\mathrm{variation}\mathrm{becomes}A=\frac{1}{2}bh. \\ Now, \\ \mathrm{When}A=36\mathrm{sq}\mathrm{cm}andb=8\mathrm{cm}: \\ 36=\frac{1}{2}\times 8\times h \\ \Rightarrow h=\frac{36\times 2}{8} \\ \Rightarrow h=9\mathrm{cm} \end{gathered}$$