Question

If in triangle ABC, AB = 6cm and DE||BC such that AE = 1/4AC, then find the length of AD . D and E are the points on AB and AC.

Answer 1

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Answer 2

Answer:

AD = 1.5 cm

Step-by-step explanation:

Consider ΔABC and DE║BC,  AB = 6cm, let AC = x the AE = $\frac{x}{4}$

Consider ΔABC and ΔADE

∠ABC= ∠ADC (corresponding angles are equal as  DE║BC)

∠BAC = ∠DAC (common angle)

Since, two angles are similar, therefore by properties of similarity of triangle,

ΔABC$\sim$ ΔADC

Also, if triangles are similar, their sides are in proportion,

∴ $\frac{AD}{AB} = \frac{AE}{EC}$

$\frac{AD}{6} = \frac{[tex]\frac{x}{4}$}{x}[/tex]

$\frac{AD}{6} = [tex]\frac{1}{4}$

AD = 1.5 cm