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Prove that in an equilateral triangle...

Prove that in an equilateral triangle, three times the square of a side is equal to four times the square of its altitudes.

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In an equilateral triangle,prove that three xx the square of one side is equal to four xx the square of one of its altitudes.

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RD SHARMA-TRIANGLES-All Questions
  1. A B C D is a rectangle. Points M and N are on B D such that A M|B D...

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  2. In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C...

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  3. Prove that in an equilateral triangle, three times the square of a ...

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  4. In a A B C , /A B C=135o . Prove that A C^2=A B^2+B C^2+4\ a r( A ...

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  5. In a quadrilateral A B C D ,\ \ /B=90o . If A D^2=A B^2+B C^2+C D^2...

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  6. In a triangle A B C , N is a point on A C such that B N|A C . If...

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  7. Nazinia is fly fishing in a stream. The tip of her fishing rod is 1...

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  8. State basic proportionality theorem and its converse.

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  9. In the adjoining figure, find A C . (FIGURE)

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  10. In the adjoining figure, if A D is the bisector of /A , what is ...

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  11. State AAA similarity criterion.

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  12. State S S S similarity criterion.

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  13. State S A S similarity criterion.

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  14. In the adjoining figure, D E is parallel to B C and A D=1c m, B D=2c m...

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  15. In the figure given below D E B C . If A D=2. 4 c m , D B=3. 6 c m...

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  16. If the areas of two similar triangles A B C and P Q R are in the ...

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  17. The areas of two similar triangles are 169\ c m^2 and 121\ c m^2 re...

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  18. If A B C and D E F are similar triangles such that /A=57o and /E=73...

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  19. If the altitude of two similar triangles are in the ratio 2:3 , wha...

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  20. If A B C and D E F are two triangles such that (A B)/(D E)=(B C)/(...

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