A lotus is $20 c m$ above the water surface in a pond and its stem is partly below the water surface. As the wind blew, the stem is pushed aside so that the lotus touched the water $40 c m$ away from the original position of the stem. How much of the stem was below the water surface originally?

Open in App

Solution

As shown in the figure,
A lotus is 20cm above the water surface in a pond
$A D = 20 c m$ ,
Height of stem below the water surface $= B D = x = ?$

The lotus touched the water $40 c m$ away from the original position of the stem,
$C D = 40 c m$

Now, in $△$ BCD,
$B C^{2} = B D^{2} + C D^{2}$
$(20 + x)^{2} = x^{2} + 40^{2}$
$(400 + x^{2} + 40 x) = x^{2} + 1600$
$40 x = 1200$
$x = 30 c m$

Hence, the stem was below the water surface originally by $30 c m$ .

Suggest Corrections

Similar questions

A lotus is 20 cm above the water surface in a pond and its stem is partly below the water surface. As the wind blew, the stem is pushed aside so that the lotus touched the water at 40 cm away from the original position of the stem. Originally how much of the stem was below the water surface? (From ‘Leelavathi’ of Bhaskaracharya).

Srivani plucked a lotus plant from a lake near her school. She observed that it has a long hollow stem. What is the function of the stem?

Why does the lotus plant have a long hollow stem?

Q. Complete the following sentence.

A hydrometer floats with half of its stem outside the water surface. It is now placed in alcohol (Relative Density

= 0.8

). The hydrometer floats with_____ than half stem inside the alcohol.

Cacti survive in a desert because:

a. It has a flat green stem to store water and prepare food by photosynthesis.

b. The stem is covered with a thick layer of cuticle, which helps to preserve water.

c. Its roots are distributed on the surface to absorb water.

d. Leaves are modified into spines to prevent loss of water

Join BYJU'S Learning Program

A lotus is 20 cm above the water surface in a pond and its stem is partly below the water surface. As the wind blew, the stem is pushed aside so that the lotus touched the water 40 cm away from the original position of the stem. How much of the stem was below the water surface originally?

A lotus is $20 c m$ above the water surface in a pond and its stem is partly below the water surface. As the wind blew, the stem is pushed aside so that the lotus touched the water $40 c m$ away from the original position of the stem. How much of the stem was below the water surface originally?