Question

In Adjoining Figure,AB||CD.Find the value of x. Class 10. Chapter Triangles.​

Answer 1

Given:

• AB || CD

To find:

Value of x = ?

Solution:

We know that AB || CD

By Alternate Interior Angles,

1. ∠ODC = ∠OBA
2. ∠OCD = ∠OAB

So, by AA similarity;

ΔOAB ∼ ΔOCD

Their corresponding sides are proportional.

$\sf{\dfrac{OA}{OC} = \dfrac{OB}{OD}}\\\\\\\Rightarrow \sf{\dfrac{3x - 19}{x - 3} = \dfrac{x-4}{4}}\\\\\\\Rightarrow \sf{4(3x-19)=(x-3)(x-4)}\\\\\\\Rightarrow \sf{12x - 76=x(x-4)-3(x-4)}\\\\\\\Rightarrow \sf{12x-76 = x^{2} -4x - 3x +12}\\\\\\\Rightarrow \sf{12x - 76 = x^{2} -7x+ 12}\\\\\\\Rightarrow \sf{x^{2} -7x+12-12x+76 = 0}\\\\\\\Rightarrow \sf{x^{2} -19x+88=0}\\\\\\\Rightarrow \sf{x^{2} -8x-11x+88=0}\\\\\\\Rightarrow \sf{x(x-8)-11(x - 8)=0}$

$\Rightarrow \sf{(x-8)(x-11)=0}\\\\\\\therefore \: \large{\boxed{\boxed{\bf{x=8 \: or \: 11}}}}$

Answer 2

Answer:

We know that AB || CD  

By Alternate Interior Angles,  

∠ODC = ∠OBA

∠OCD = ∠OAB

So, by AA similarity;  

ΔOAB ∼ ΔOCD