Question

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

Answer 1

Step-by-step explanation:

Refer to the attachment...

Answer 2

Step-by-step explanation:

given

equilateral triangle ABC with each side a and a d as one of its altitude

to prove

3 into square of one side is equal to 4 into square of one side of its amplitude

therefore 3apower of 2 equal to 4ad too the power of 2

proof

in triangle ADB and triangle is d c a b equal to AC( both as its amplitude),a d equal to a d (common side ). angle adb equal to angle a d c equal to 90 degree

is triangle ADB equal to triangle ADC is equal to by RHS congruence

BC equal to DC cpct

BC equal to DC equal to half of DC BC equal to DC is equal to 1 by 2

now ADB is a right angle triangle using Pythagoras theorem

hypotenuse square equal to height square + base square

ab square equal to ad square +bd square

a square equal to A D square + of a whole to the power of square

a square is equal to a square + a by four square

a square minus A square by 4 equal to 80 square .

four square minus A square by 4 equal to a square

3 a square by 4 equal to a square

a square equal to 4 into square

3 a square equal to 4ad square