Question

In the figure given in attachment, AB, EF and CD are parallel lines. Given that AB = 15 cm, EG = 5 cm, GC = 10 cm and DC = 18 cm. Calculate
(i) EF
(ii) AC

Topic- Similarity
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Answer 1

Answer :-

(i) EF = 9 cm

(ii) AC = 25 cm

Explanation :-

In the given figure, we have :-

→ AB || EF || CD

→ AB = 15 cm ; EG = 5 cm

→ GC = 10 cm ; DC = 18 cm

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Firstly let's consider ∆EFG and ∆CDG . [EF || DC]

⇒ ∠EGF = ∠CGD (Vertically opp. ∠s)

⇒ ∠EFG = ∠CGD (alternate ∠s)

∴ ∆EFG ~ ∆CDG (by AA- criterion)

For these similar triangles we have :-

⇒ EF/EG = DC/GC

⇒ EF/5 = 18/10

⇒ EF = 1.8 × 5

⇒ EF = 9 cm

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Now let's consider ∆ABC and ∆EFC . [AB || EF]

⇒ ∠ACB = ∠ECF (common ∠s)

⇒ ∠ABC = ∠EFC (corresponding ∠s)

∴ ABC ~ ∆EFC (by AA- criterion)

Again for these similar triangles :-

⇒ AC/EC = AB/EF

⇒ AC/(EG + GC) = AB/EF

⇒ AC/(10 + 5) = 15/9

⇒ AC = (15 × 15)/9

⇒ AC = 225/9

⇒ AC = 25 cm

Answer 2

Answer:

$\sf\tt\large{\blue {\underline {\underline{⚘\;Question:}}}}$

• AB,EF,CD are the parallel lines. Given that,
• AB=15cm.
• EG=5cm
• GC=10cm
• DC=18cm.

Calculate :

1. EF
2. AC.

$\sf\tt\large{\purple {\underline {\underline{⚘\;Answer: }}}}$

$\sf\tt\large{\green {\underline {\underline{⚘\;The \;value \;of \;EF=9cm:}}}}$

$\sf\tt\large{\green {\underline {\underline{⚘\;The \;value \;of\;AC=25cm:}}}}$

$\sf\tt\large{\red {\underline {\underline {⚘\;Solution:}}}}$

• Refer the given attachment for better understanding.

Hope it helps u.

Thank you .