Question

The ratio of the area of two triangles of the same height is equal to the ratio of their bases.

Enter 1 for True 0 for False

Answer 1

Area of a triangle $=\frac{1}{2}\times$ Base $\times$ Height
Given that the heights of two triangles are equal.
Let $b_1$ & $b_2$ are bases of two different triangle and $h_1$ & $h_2$ are heights of these two triangle.
Then, $h_1=h_2$
Now,
$\frac{Areaof1sttriangle}{Areaof2ndtriangle}=\frac{\frac{1}{2}\times b_1\times h_1}{\frac{1}{2}\times b_2\times h_2}$
$=>\frac{Areaof1sttriangle}{Areaof2ndtriangle}=\frac{b_1\times h_2}{b_2\times h_2}$ $[h_1=h_2]$
$=>\frac{Areaof1sttriangle}{Areaof2ndtriangle}=\frac{b_1}{b_2}$