Question

Solve for x.
A)

5

B)

10

C)

8

D)

14

Answer 1

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

Given that, In triangle UWZ,

• VY || WZ

• UY = 5x

• YZ = 10

• UV = 20

• VW = 8

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, using Basic Proportionality Theorem, we have

$\rm \: \dfrac{UY}{YZ} = \dfrac{UV}{VW}$

$\rm \: \dfrac{5x}{10} = \dfrac{20}{8}$

$\rm \: \dfrac{x}{2} = \dfrac{5}{2}$

$\red{\rm\implies \:\boxed{ \rm{ \:x \: = \: 5 \: \: }}}$

So, option (A) is correct.

$\rule{190pt}{2pt}$

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.

Answer 2

Answer:

x=5

Step-by-step explanation:

Given:-

In triangle UWZ,

VY || WZ

UY = 5x

YZ = 10

UV = 20

VW = 8

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.

we have,

UY/YZ = UV/VW

⇒ 5x/10 = 20/8

⇒ x/2= = 5/2

⇒ 2x = 10

⇒ x = 10/2

⇒ x = 5

$\pink{\boxed{x=5}}$