Question

In a triangle ABC , DE is a line parallel to BC . If AC= 6.4cm, AE= 4cm,BC= 3.5 cm and BD = 3cm. Find AD and DE.

Answer 1

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Answer 2

Length of AD = x = 5 cm

Length of DE = 1.75 cm

Step-by-step explanation:

Δ ADE ≅ ΔABC

$\frac{AD}{AB} = \frac{AE}{AC}$

$\frac{x}{3 + x} = \frac{4}{6.4}$

$\frac{x}{3 + x} = \frac{5}{8}$

$8x = 15 + 5x$

$3x = 15$

⇒ x = 5 cm

Length of AD = x = 5 cm

Since DE ║ BC & D & E are the mid points of AB & AC. Thus

$DE=\frac{BC}{2}$

$DE = \frac{3.5}{2}$

$DE = 1.75$ cm

Thus the length of DE = 1.75 cm