A lotus flower is blooming in a lake. The flower is 1/2 meters above the surface of the lake.when the western wind blows the flower droops at a distance of 2m from the base. Find the depth of the lake.
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depth of lake is 4 m
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Given:A lotus flower is blooming in a lake . The flower is
1
2
12metres above the surface of the lake. When the western wind blows, the flower drops at a distance of
2
2 metres from the base.
To find:depth of the lake.
The lotus flower is
1
2
12 m above the surface of the lake. Let us assume water has a depth
y
y, then length of the stem will be
(
y
+
1
2
)
(y+12). The length of the stem is same. Now the distance of stem from original position(base) is
2
2 m
Taking water to be horizontal and stem to be straight(right angle(imagination),
Using pythagoras theorem we have,
(
y
+
1
2
)
2
=
y
2
+
2
2
(y+12)2=y2+22
⇒
y
2
+
1
4
+
2.
y
.
1
2
=
y
2
+
4
⇒y2+14+2.y.12=y2+4
⇒
y
2
+
4
=
y
2
+
1
4
+
y
⇒y2+4=y2+14+y
⇒
y
=
4
−
1
4
⇒y=4−14
⇒
y
=
15
4
⇒y=154
⇒
y
=
3.7
⇒y=3.7 m
∴
∴ Depth of lake is
3.7
3.7 m
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