Question

plz tell me fast i have to complete my test plz

Answer 1

Given :-

In triangle ABC,

• DE || BC

• AD = x

• DB = 3x + 4

• AE = x + 3

• EC = 3x + 19

To Find :-

• Value of x

Solution :-

Given that,

In triangle ABC,

• DE || BC

• AD = x

• DB = 3x + 4

• AE = x + 3

• EC = 3x + 19

We know,

↝ 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.

So,

↝ By Basic Proportionality Theorem,

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

$\rm :\longmapsto\:\dfrac{x}{3x + 4} = \dfrac{x + 3}{3x + 19}$

$\rm :\longmapsto\:x(3x + 19) = (x + 3)(3x + 4)$

$\rm :\longmapsto\: {3x}^{2} + 19x = {3x}^{2} +9x + 4x + 12$

$\rm :\longmapsto\:19x = 13x + 12$

$\rm :\longmapsto\:19x - 13x = 12$

$\rm :\longmapsto\:6x = 12$

$\bf\implies \:x = 2$

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.