Question

In a quadrilateral traingle, prove that three times the square of one wide is equal to four times the square of one of it's altitude​

Answer 1

Answer:

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. [Pythagoras theorem]

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.

In ΔABC,

AB = BC = CA (sides of the triangle), AD is the altitude

AD ⊥ BC

We know that in an equilateral triangle perpendicular drawn from vertex to opposite side bisects the side

Thus, BD=CD=BC2

Now in ΔADC,

AC2=AD2+CD2

⇒BC2=AD2+(BC2)2[Since AC = BC and CD=BC2]

⇒(BC)2=(AD)2+(BC)24

⇒(BC)2−(BC)24=(AD)2

⇒3(BC)24=AD2

⇒3(BC)2=4(AD)2