Question

In a lake of Botanical garden the tip of lotus was seen 2 cm above the surface of water. Being forced by the wind, it gradually advanced amd submerged at a distance of 15 cm from the previous position. Let us write by calculating the depth of water.​

Answer 1

Answer :-

The depth of the water is 55.25 cm.

Explanation :-

Given :

The tip of lotus was seen above the surface of water at 2 cm.

Then, It submerged at a distance of 15 cm.

To find :

The depth of water

Solution :

Let the perpendicular AB be x cm

Then, the hypotenuse AD is (x+2) cm

And the base = 15 cm

(AC=AD)

We will solve the question by the Pythagorean theorem:-

Hypotenuse² = Perpendicular ² + Base²

=> AD² = AB² + BD² cm

=> (x+2)² = x² + 15² cm

=> x² + 4x + 4 = x² + 225 cm

=> 4x + 4 = 225 cm

=> 4x = 225 - 4 cm

=> 4x = 221 cm

=> x = 221/4 cm

=> x = 55.25 cm

Hence, the depth of the water is 55.25 cm.

Answer 2

Step-by-step explanation:

Let x=depth of the water

OL=x +2

Therefore,OL' =(X+2)CM

AL'=15 CM

IN ryt angled OAL'

By Pythagoras Theorem

OL'=OA²+AL²

(X+2)=X²+15²

X²+4+4x=x² +225

Therefore, 4 x = 225 -1 =221

x = 221 /4

or, x =55 1/4.

Answer : the depth of the water is 55 1/4cm