Question

ABC is an equilateral triangle in which DE parallel to BC.if AE/Ec=1/2 and BC=9cm find DB

Answer 1

Answer:

Your answer is in the pic

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Answer 2

The value DB is 6cm.

Given:

ABC is an equilateral triangle and DE||BC.

To Find:

The value of DB.

Solution:

Since DE is parallel to one side of a triangle and intersects other two sides.

By Basic  Proportionality Theorem

$\frac{AD}{DB} =\frac{AE}{EC} \\\\\frac{AD}{DB} = \frac{1}{2} \\\\\frac{AB-DB}{DB} = \frac{1}{2}$

∵ From diagram AD=AB-DB and Also it is a equilateral triangle ,AB=BC

∴ AD=BC-DB

= 9-DB

$\frac{9-DB}{DB} =\frac{1}{2} \\\\\frac{9}{DB} -1 = \frac{1}{2} \\\\\frac{9}{DB}= \frac{1}{2}+1\\\\\frac{9}{DB}= \frac{3}{2}\\\\DB= 9 \times \frac{2}{3} \\\\DB = 6$

Therefore, The value DB is 6cm.

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