Question

In ∆ ABC , DE||BC . find the value of AE .

pls answer step by step


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Answer 1

Answer:

value of AE = 2.4cm

Step-by-step explanation:

consider ∆ABC and ∆ADE

angle <BAC = angle <DAE ( common angle)

since DE||BC corresponding angles are equal Angle <ABC = angle <ADE

By AA criteria ∆ABC ~∆ADE

By basic proportionality theorem

AB/AD = BC/DE = AC/AE

Let AE = x

$\frac{1.8 + 5.4}{1.8} = \frac{x + 7.2}{x} \\ \frac{7.2}{1.8} = \frac{x + 7.2}{x} \\ 4x = x + 7.2 \\ 4x - x = 7.2 \\ x = 7.2 \div 3 \\ x= 2.4$