Math, asked by mohak81, 8 months ago

A girl of height 90 cm is walking away from the base of the lamp post at a speed of 1.2 m/sec. If the lamp post is 3.6 m above the ground, find the length of her shadow after 4 seconds.​

Answers

Answered by Anonymous
220

Qᴜᴇsᴛɪᴏɴ :-

A girl of height 90 cm is walking away from the base of the lamp post at a speed of 1.2 m/sec. If the lamp post is 3.6 m above the ground, find the length of her shadow after 4 seconds.

Gɪᴠᴇɴ :-

  • Height of the lamp post = 3.6 m
  • Speed of the girl = 1.2 m/sec

Tᴏ Fɪɴᴅ :-

  • Length of her shadow after 4 seconds

Sᴏʟᴜᴛɪᴏɴ :-

ʀᴇғᴇʀ ᴛʜᴇ ᴀᴛᴛᴀᴄʜᴍᴇɴᴛ ғᴏʀ ᴛʜᴇ ᴅɪᴀɢʀᴀᴍ

Distance travelled in 4 sec = Speed × Time

1.2 × 4

4.8 m

480 cm

  • Height of the girl (CD) = 90 cm

Let the length of the shadow at a distance of 4.8m from the lamp post = x cm

From the diagram,

∆ABE ∼ ∆DCE

∠B = ∠C = 90°

∠E = ∠C common

(A.A. similarity)

Hence, AB/DC = BE/CE = AE/DE

360/90 = 480 + x / x

➸ 4 = 480 + x / x

➸ 4x = 480 + x

➸ 4x - x = 480

➸ 3x = 480

➸ x = 480/3

➸ x = 160cm

➸ x = 1.6m

⛬ Length of the shadow = 1.6 m

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Answered by Anonymous
80

Qᴜᴇsᴛɪᴏɴ

✯.A girl of height 90 cm is walking away from the base of the lamp post at a speed of 1.2 m/sec. If the lamp post is 3.6 m above the ground, find the length of her shadow after 4 seconds.

\large\underline\bold{GIVEN,}

\sf\dashrightarrow height\:of\:the\:lamp=3.6m(360CM)

\sf\dashrightarrow height\:of\:the\:girl\:90cm

\sf\dashrightarrow speed\:of\:the\:girl\:1.2 m/s

\large\underline\bold{TO\:FIND,}

\sf\dashrightarrow LENGTH\:OF\:HER\:SHADOW\:AFTER\:4\:SECONDS

FORMULA IN USED,

\sf\therefore  DISTANCE=SPEED \times TIME

\large\underline\bold{SOLUTION,}

\large{\boxed{\bf{please\:refer\:the\:given\:diagram }}}

\sf\therefore time=4\:seconds

\sf\implies d=1.2 \times 4

\sf\implies d=4.8cm

✯conversion,

\sf\therefore centimetre \:into\:metre

\sf\implies 4.8cm

\sf\implies 1m=100cm

\sf\implies 480cm

\large{\boxed{\bf{480\:CM}}}

✯ACCORDING TO THE QUESTION,

\sf\therefore LET \:US\:ASSUME\:THE\:LENGTH\:OF\:THE\:SHADOW\:AS\:"X"

\sf\therefore height\:of\:the\:girl\:90cm

\sf\therefore NOW,\:IN\:TRIANGLE\: \triangle ABE \:and \: \triangle DCE

\sf\implies \angle B= \angle C.....90\degree \:each

\sf\implies \angle E= \angle C ......common

\sf\implies \triangle ABE \sim \triangle ...... A.A. RULE CRITERIA

THEREFORE,

\sf\implies \dfrac{AB}{DC}= \dfrac{BE}{CE}= \dfrac{AE}{DE}

NOW,

\sf\implies \dfrac{360}{90}=  \dfrac{480+x}{x}

\sf\implies \dfrac{\cancel{360}}{\cancel{90}}= \dfrac{480+x}{x}

\sf\implies 4x=480+x

\sf\implies 4x-x=480

\sf\implies 3x=480

\sf\implies \dfrac{480}{3}

\sf\implies \cancel \dfrac{480}{3}

\sf\implies 160cm

✯FROM CM TO M,

\sf\implies 1.6M

\sf{\boxed{\bf{ LENGTH\:OF \:SHADOW=1.6M}}}

_________________________

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