Some kindergarten students were playing near a lamppost. They were so excited to see their
shadows and trying to show that their shadow is the longest. The lamp was 3.6 m above the
ground. One of the girl of height 90 cm was walking away from the base of a lamppost at a speed
of 1.2 m/s.
(i) Which of the following line segment shows the length of the shadow?
(a) CE
(b) BE
(c)DE
(d) CD
(ii) What would be the length of her shadow after 4 seconds?
(a) 1.2 m
(b) 1.6 m
(c)2.3 m
(d) 1.4 m
(iii) How far is the girl from the lamppost?
(a) 4.8 m
(b) 1.2m
(c) 3.6 m
(d) 6.4 m
(iv) ∆ABE and ∆CDE are similar because:
(a) All sides are equal.
(b) The shadow of the girl is equal to the height of the lamppost.
(c) ZB and ZE are equal and one angle is common.
et ZB and 2D are equal and one angle is common.
(v) What would be length of her shadow after 6 seconds?
(a) 4.8 m
(b) 2.4 m
(c) 3.6 m
(d) 6.4 m
Answers
Answer:
1. DE
2. 1.6M
3. 4.8M
4. BOTH ARE RELATED TO THE SAME LENGTH OF THE SHADOW
5. LAMPOST,THE GIRL
Concept:
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "~"
Given:
Some kindergarten students were playing near a lamppost. They were so excited to see their
shadows and trying to show that their shadow is the longest. The lamp was 3.6 m above the
ground. One of the girl of height 90 cm was walking away from the base of a lamppost at a speed
of 1.2 m/s
Find:
(i) Which of the following line segment shows the length of the shadow?
(a) CE
(b) BE
(c)DE
(d) CD
(ii) What would be the length of her shadow after 4 seconds?
(a) 1.2 m
(b) 1.6 m
(c)2.3 m
(d) 1.4 m
(iii) How far is the girl from the lamppost?
(a) 4.8 m
(b) 1.2m
(c) 3.6 m
(d) 6.4 m
(iv) ∆ABE and ∆CDE are similar because:
(a) All sides are equal.
(b) The shadow of the girl is equal to the height of the lamppost.
(c) ZB and ZE are equal and one angle is common.
et ZB and 2D are equal and one angle is common.
(v) What would be length of her shadow after 6 seconds?
(a) 4.8 m
(b) 2.4 m
(c) 3.6 m
(d) 6.4 m
Solution:
AB=3.6m
DE=0.9m
After 4 seconds,
BE=1.2x4=4.8
Let CE=x
and ∠DCE=α
So, tanα=DE/CE
=0.9/x
Again,tanα=AB/BC
⇒0.9/x=3.6/4.8+x
⇒4.32+0.9x=3.6x
⇒4.32=2.7x
⇒x=1.6m
∆ABE and ∆CDE are similar because:
∠DEC=∠ABC (∵right angle)
∠DCE=∠ACB(∵Common angle)
By AA similarity,
we can write, DE/AB=CE/BC
(v)After 6 seconds,
BE=1.2x6=7.2
Let CE=x
and ∠DCE=α
So, tanα=DE/CE
=0.9/x
Again,tanα=AB/BC
⇒0.9/x=3.6/7.2+x
⇒6.48+0.9x=3.6x
⇒6.48=2.7x
⇒x=2.4m
Therefore,
1. DE
2. 1.6M
3. 4.8M
4. BOTH ARE RELATED TO THE SAME LENGTH OF THE SHADOW
5. 2.4m
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