Question

the hypotenuse of a right angled triangle is 25 cm if one side 5m more than the other side find its area

Answer 1

Solution :-

There is a mistake in this question. The length of one of the two sides must be 5 cm instead of 5 m.

Let smaller side of the right angled triangle be x cm

Then, the other side will be (x + 5) cm

Using Pythagoras Theorem -

(Hypotenuse)² = (Base) + (Perpendicular)²

⇒ (25)² = (x)² + (x + 5)²

⇒ 625 = x² + x² + 10x + 25

⇒ 2x² + 10x - 625 + 25 = 0

⇒ 2x² + 10x - 600 = 0

⇒ x² + 5x - 300 = 0

⇒ x² + 20x - 15x - 300 = 0

⇒ x(x + 20) - 15 (x + 20) = 0

⇒ (x - 15) (x + 20) = 0

⇒ x = 15, x = - 20

x cannot be negative. So, x = 15 cm

Other side of the triangle will be 15 + 5 = 20 cm

The two sides of the given triangle are 15 cma nd 20 cm

Now, 

Area of the given triangle = 1/2*Base*Height

⇒ 1/2*15*20

⇒ 300/2

= 150 cm²

So, area of the given triangle is 150 cm²

Answer.