Question

the areas of two Triangles are equal and the ratio of their bases is X:Y then the ratio of their Heights is

Answer 1

Answer:

The ratio of the heights of the triangles is Y : X.

Step-by-step explanation:

It is given that the area of two triangles is equal and the ratio of their bases is X : Y.

Let the two triangles are ΔABC( from which X belongs ) and ΔPQR( from which Y belongs ),

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From the properties of triangle, we know : -

Area of triangle = 1 / 2 x base x height

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Then,

Let the bases of ΔABC and ΔPQR are base₁ and base₂ respectively, and the  heights of the ΔABC and ΔPQR are height₁ and height₂ respectively.

According to the question : -

⇒ Area of ΔABC = area of ΔPQR

= > 1 / 2 x base₁ x height₁ = 1 / 2 x base₂ x height₂

= > base₁ x height₁ = base₂ x height₂

= > base₁ / base₂ = height₂ / height₁

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Given,

       Ratio of bases is X : Y

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= > X / Y = height₂ / height₁

= > height₁ / height₂ = Y / X

Hence, ratio of their heights is Y : X.