Question

The height of the tree when its shadow is 84m long and at the same time a girl 2m high standing in the same straight line casts a shadow 12m is
a)14m
b)24m
c)6m
d)12m

plzz answer me fast
its urgent​

Answer 1

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$\frac{84}{h}=\frac{12}{2}$

$\mathtt{h=14\:m}$

Answer 2

Answer:

The correct answer is option(a)14m

Step-by-step explanation:

Given,

Length of the shadow of tree = 84m

Height of the girl = 2m

Length of the shadow of the girl = 12m

To find,

The height of the tree

Recall the concepts

AA similarity theorem:

If any two angles of one triangle are equal to the corresponding angles of another triangle, then the two triangles are similar.

If two triangles are similar, then their corresponding angles will be equal and the corresponding sides will proportional

Solution:

Let the tree be BC and The shadow of the tree be AB

Again let the girl be PQ and the shadow of the girl be AP

Then we have

AB = 84m

PQ = 2m

AP = 12m

Required to find the value of BC

Let us consider the two triangles ABC and APQ

We have ∠ABC = ∠APQ = 90°

∠A is common to both the triangles

By AA similarity theorem, ΔABC and ΔAPQ are similar

Since ΔABC and ΔAPQ are similar, the corresponding sides of the triangle will be proportional

$\frac{AP}{AB} = \frac{PQ}{BC}$

Substituting the values, we get

$\frac{12}{84} = \frac{2}{BC}$

12× BC = 2 ×84

BC = $\frac{2 X 84}{12}$ = 14m

The height of the tree = 14m

Hence the correct answer is option(a)14m

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