Question

D and E are the points on side AB and AC of a triangle ABC,respectively and AD= 6cm, BD = 12cm, EC = 8cm. If DE || BC, then the length of AE is


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Answer 1

Question :-

D and E are the points on side AB and AC of a triangle ABC,respectively and AD= 6cm, BD = 12cm, EC = 8cm. If DE || BC, then the length of AE is ?

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Solution :-

➲ Given Information :-

• ABC is a Triangle
• Point D lies on side AB
• Point E lies on side AC
• Length of AD ➢ 6 cm
• Length of BD ➢ 12 cm
• Length of EC ➢ 8 cm
• DE || BC

➲ To Find :-

• Length of AE

➲ Concept :-

• Quadrilaterals

➲ Theorm Used :-

• Basic Proportionality Theorem

➲ Explanation :-

• In this question, First of all we will be finding the Length of side AB and since, DE || BC, Using The Basic Proportionality Theorem, We will equate side AB and side AC. Then solving further will give us the Length of AE. Which is to be found.

➲ Diagram :-

• Kindly refer to the image given above in the attachment.

➲ Calculation :-

∵ AD = 6 cm And DB = 12 cm

:⇒ Finding the Length of side AB = Length of AD + Length of DB

Substituting the values here, We get,

:⇒ Length of side AB = 6 cm + 12 cm

:⇒ Length of side AB = 18 cm

∵ DE || BC,

∴ Using The Basic Proportionality Theorem, We get,

$\sf : \implies \boxed{\boxed{\sf{\red{\dfrac{AD}{DB} = \dfrac{AE}{CE} }} }}$

Substituting the values here, We get,

$\sf: \implies \dfrac{6}{12} = \dfrac{AE}{8}$

Transposing 8 to Right Hand Side of the equation, in the numerator, We get,

$\sf: \implies AE = \dfrac{6 \times 8}{12}$

Cancelling & Calculating further, We get,

$\sf: \implies\boxed{\boxed{ \sf{AE = \red{4 \: cm}}}}$

∴ Length of AE = 4 cm

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Final Answer :-

• The Length of AE is 4 cm.

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