Question

Find the value of h in the diagram given below.​

Answer 1

/* There is a mistake in the question. It must be like this . */

$\triangle {ABC} \sim \triangle {ADE}$

$AB = 6 \:m , BD = 12 \:m , CB = 0.9 \:m$

$\red{h = ? }$

$If \: \triangle {ABC} \sim \triangle {ADE}$

$\frac{DE}{BC} = \frac{AD}{AB}$

$\blue{ ( Corresponding \:sides \:are \:in \:the \:same \:ratio )}$

$\implies \frac{DE}{BC} = \frac{AB+BD}{AB}$

$\implies \frac{h}{0.9} = \frac{6 + 12}{6}$

$\implies \frac{h}{0.9} = \frac{18}{6}$

$\implies h = 3 \times 0.9$

$\implies h = 2.7 \:m$

Therefore.,

$\red{ Value \: of \: h } \green { = 2.7 \:m}$

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Answer 2

h = 2.7 m.

Solution :-

In ΔABC & Δ ADE ,

• ∠ABC =~ ∠ADE (Corresponding angle)
• ∠ACB =~ ∠AEB (Corresponding angle)

.°. ΔABC =~ Δ ADE (By AA test)

=> BC / DE = AB / AD ( Corresponding sides are in the same ratio)

=> BC / DE = AB / AB + BD ( A-B-D)

=> 0.9 / h = 6 / 6 + 12

=> 0.9 / h = 6 / 18

=> h = 0.9 × 18 / 6

=> h = 16.2 / 6

=> h = 2.7

Hence, h = 2.7 m.