Question

If two triangles have equal area and the ratio of their bases is equal to $2:3$, then find the ratio of the corresponding altitudes.

Answer 1

Area of first triangle=Area of second triangle

=$\frac{1}{2}\times B_1\times h_1=\frac{1}{2}\times B_1\times h_2$

$=\frac{B_1}{B_2}=\frac{h_2}{h_1}$

$=\frac{2}{3}=\frac{h_2}{h_1}$

$=\frac{h_1}{h_2}=\frac{3}{2}$

Ratio of their altitudes=$3:2$