triangle

Let ΔPQR be the right angled triangle, and PQR = 90,

Area of an equilateral triangle = 3x(Side)²/4

The area of equilateral triangle on side PQ = 3xPQ²/4

The area of equilateral triangle on side QR = 3xQR²/4

The area of equilateral triangle on side PR = 3xPR²/4

Using Pythagoras' Theorem,

PR2 = PQ2 + QR2,

Multiplying both sides by  3/4

(3/4)PR² = (3/4)PQ² + (3/4)QR²,

Area of E. triangle on hypotenuse, PR = Area of E. triangle on side PQ +  Area of E. triangle on side QR ]

Regards,

Team,

TopperLearning.