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

True

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False

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Solution

The correct option is A
True

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-2having 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 the same area, c = d

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Similar questions

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

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

Two triangles have equal area of $24 c m^{2}$ and stand on the same base of 6 cm, if the distance PQ (on base) between their altitudes is equal to the length of one of the altitude. Then the area of quadrilateral formed by the altitudes and the base PQ is equal to:

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and stand on the same base of 6 cm. If the distance PQ between their altitudes is equal to the length of one of the altitude, then the area of quadrilateral formed by the altitudes and the base PQ is equal to:___.

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