In the given figure $ riangle$ ABC is shown, in which DE $\paralle...

Question

In the given figure $	riangle$ ABC is shown, in which DE $\parallel$ BC. If AD = 5 cm, DB = 2$\cdot$5 cm and DE = 8 cm, then the length of BC is :

*(Figure : D lies on AB and E lies on AC, with DE parallel to BC.)*

Accepted Answer

**Step 1 — Find AB.**
$$AB = AD + DB = 5 + 2{\cdot}5 = 7{\cdot}5 	ext{ cm}$$

**Step 2 — Show the triangles are similar.**
Since $DE \parallel BC$ :
$\angle ADE = \angle ABC$ and $\angle AED = \angle ACB$ (corresponding angles)
$$	herefore\ 	riangle ADE \sim 	riangle ABC \quad (	ext{AA similarity})$$

**Step 3 — Use the ratio of corresponding sides.**
$$\frac{AD}{AB} = \frac{DE}{BC}$$

**Step 4 — Substitute and solve.**
$$\frac{5}{7{\cdot}5} = \frac{8}{BC} \ \Rightarrow\ BC = \frac{8 	imes 7{\cdot}5}{5} = \frac{60}{5} = 12 	ext{ cm}$$

**Answer : (C) 12 cm**

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