Question

इन न इक्विलैटरल ट्रायंगल प्रोव ठाट थ्री टाइम्स द स्क्वायर ऑफ वन साइड इज इक्वल टू 40 स्क्वायर ऑफ वन आफ इट्स एल्टीट्यूड English language​

Answer 1

$\mathbf{\color{purple}{\huge{✮}}}\mathbf{\blue{\huge{A}}}\mathbf{\color{aqua}{\huge{N}}}\mathbf{\green{\huge{S}}}\mathbf{\color{yellow}{\huge{W}}}\mathbf{\orange{\huge{E}}}\mathbf{\red{\huge{R}}}\mathbf{\color{maroon}{\huge{✮}}}$

Given:-

An equilateral triangle with one of its altitude.

Solution :-

Let a be the side of the equilateral triangle.

∴BE=EC= 2BC = 2a

To prove:- 4AE 2 =3a2

In △ABE, by pythagoras theorem

AB 2 =AE 2 +BE 2a 2 =AE 2 +( 2a ) 2

⇒AE 2 =a 2 − 4a 2

⇒AE 2 = 44a 2 −a2

⇒AE 2 = 43a 2

⇒4AE 2 =3a 2

Hence proved that three times the square of one side is equal to four times the square of one of its altitudes.

$\huge{\underline{\boxed{\purple{{★ Hence \: Verified ★}}}}}$