Question

17. From the given figure AABC, DE II BC, AD= 1.5 cm,
DB=6 cm, AE = x cm, EC = 8 cm, then x =
А
D
E
B В
C С
A) 2.5 cm
B) 2 cm
C) 3 cm
D) 3.5 cm​

Answer 1

Answer:

14

Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Solution-}}$

Given :-

A triangle ABC, D and E are points on AB and AC such that

• DE || BC

• AD = 1.5 cm

• DB = 6 cm

• AE = x cm

• EC = 8 cm

We know,

By Basic Proportionality Theorem,

• If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.

Therefore,

$\rm :\longmapsto\:\dfrac{AD}{DB} = \dfrac{AE}{EC}$

$\rm :\longmapsto\:\dfrac{1.5}{6} = \dfrac{x}{8}$

$\rm :\longmapsto\:\dfrac{15}{60} = \dfrac{x}{8}$

$\rm :\longmapsto\:\dfrac{1}{4} = \dfrac{x}{8}$

$\bf\implies \:x = 2 \: cm$

$\purple{\bf\implies \:Option \: (B) \: is \: correct}$

$\large\boxed{ \green{\bf{Additional \: Information}}}$

1. Pythagoras Theorem :-

• This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

• This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

• This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.