A lotus flower is blooming in a lake. The flower is $\frac{1}{2}$ meter above the surface above the lake. When the western wind blows, the flower drops at a distance of $2 m$ from the base. Find the depth of the lake.

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Solution

Given:A lotus flower is blooming in a lake . The flower is $\frac{1}{2}$ metres above the surface of the lake. When the western wind blows, the flower drops at a distance of $2$ metres from the base.
To find:depth of the lake.
The lotus flower is $\frac{1}{2}$ m above the surface of the lake. Let us assume water has a depth $y$ , then length of the stem will be $(y + \frac{1}{2})$ . The length of the stem is same. Now the distance of stem from original position(base) is $2$ m
Taking water to be horizontal and stem to be straight(right angle(imagination),
Using pythagoras theorem we have,
${(y + \frac{1}{2})}^{2} = y^{2} + 2^{2}$
$\Rightarrow y^{2} + \frac{1}{4} + 2. y . \frac{1}{2} = y^{2} + 4$
$\Rightarrow y^{2} + 4 = y^{2} + \frac{1}{4} + y$
$\Rightarrow y = 4 - \frac{1}{4}$
$\Rightarrow y = \frac{15}{4}$
$\Rightarrow y = 3.7$ m
$∴$ Depth of lake is $3.7$ m

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A lotus flower is blooming in a lake. The flower is 12 meter above the surface above the lake. When the western wind blows, the flower drops at a distance of 2 m from the base. Find the depth of the lake.

A lotus flower is blooming in a lake. The flower is $\frac{1}{2}$ meter above the surface above the lake. When the western wind blows, the flower drops at a distance of $2 m$ from the base. Find the depth of the lake.