Question

Find the value of x, which will make PQ || AB in the given figure
1 point
А
A
B В
3x+19
3x+4
P Р
x+3
a
с c

Answer 1

Given:

• AP = 3x + 19
• PC = x + 3
• BQ = 3x + 4
• QC = x

To find:

⟶ Value of x

Solution:

Applying Basic Proportionality theorem,

$\bf{\dfrac{3x+19}{x+3} = \dfrac{3x+4}{x}}$

$\rm{On\:Cross\:Multiplication,}$

$\sf{x(3x+19) = (x+3)(3x+4)}\\\\\Rightarrow \sf{3x^{2} + 19x = x(3x+4)+3(3x+4)}\\\\\\\Rightarrow \sf{3x^{2} +19x=3x^{2} +4x+9x+12}\\\\\\\Rightarrow \sf{3x^{2} +19x = 3x^{2} +13x+12}$

$\rm{Cancelling\: 3x^{2} \: on \: both \: sides;}$

$\sf{19x = 13x+12}\\\\\\\Rightarrow \sf{19x-13x=12}\\\\\\\Rightarrow \sf{6x=12}\\\\\\\Rightarrow \sf{x = \dfrac{12}{6}}\\\\\\\therefore \large{\boxed{\boxed{\bf{x = 2}}}}$

Know more:

• Basic Proportionality theorem states that If a line is drawn parallel to one side of a triangle, intersecting the other 2 sides in distinct points, then the other 2 sides are divided in the same ratio.

Answer 2

Answer:

2 is the answer of thel question