Question

If two triangles have equal area and stand on the same base, then the altitudes of triangle are equal.

• A. 1: AB-b; 2: AD-a; 3: BC-c
• B. 1: AB-a; 2: AD-b; 3: BC-c

Answer 1

The correct option is A

1: AB-b; 2: AD-a; 3: BC-c

Triangles on the same base (or equal bases) and having equal areas have equal altitudes.

This can be easily proved. Take two triangles: triangle-1 and triangle-2 having same base 'b' and altitudes 'c' and 'd' respectively.

Area of Triangle-1 = $\frac{1}{2}\times b\times c$

Area of Triangle-2 = $\frac{1}{2}\times b\times d$

Since, the triangles have same area, c = d