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In an equilateral triangle, prove that t...

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

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KALYANI PUBLICATION-PYTHAGORAS THEOREM-EXERCISE
  1. ∆ABC is a right angled at B and D is mid-point of BC. Prove that AC^2 ...

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  2. ∆PQR is right angled at Q and the points S and T trisect the side QR. ...

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  3. In an equilateral triangle, prove that three times the square of one s...

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  4. In an equilateral triangle ABC, D is a point on side BC such that BD =...

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  5. ∆ABC is right angled at C and CD | AB. If BC = a , CA=b , AB = c and C...

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  6. Of triangle ABC,angleB=90^@ and BD|AC.IF AB=c,BC=a,CA=b and BD=p then ...

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  7. Two poles of heights 6 m and 11 m stand on a plane ground. If the dist...

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  8. Two poles of height 10 m and 15 m stand vertically on a plane ground. ...

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  9. In Fig.6.45,O is a point in the interior of a triangle ABC,OD|BC,OE|AC...

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  10. O is a point in the interior of ∆ABC. OD,OE and OF are the perpendicul...

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  11. O is any point inside a rectangle ABCD. Prove that OB^2+OD^2=OA^2+OC^2...

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  12. Prove that the sum of the squares of the sides of a rhombus is equal t...

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  13. A ship rail 25 km due south and then 60 km due west. How far it is the...

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  14. B is due west of A and C is due north of B. If the distance between B ...

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  15. A man travels 27 km due south then 24 km due west. Finally 20 km due n...

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  16. An aeroplane leaves an airport and flies due north at a speed of 1000 ...

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  17. In an isosceles triangle ABC if AC=BC and AB^2 = 2AC^2, prove that /C ...

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  18. The length of the sides of a triangle are ax-by,ay+bx and sqrt((a^2+b^...

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  19. The length of the sides of a triangle are a+b,ab-1 and sqrt((a^2+1)(b^...

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  20. In the triangle ABC, BC = m^2 -n^2, AC =3 mn and AB = m^2+n^2. Prove t...

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