Answer:
Therefore the value of x is
[tex]x=5[/tex]
Step-by-step explanation:
Given:
Consider the figure such that
PQ || BC
AP = 20 , AB = 36
AQ = 5x , AC = 45
To Find:
x = ?
Solution:
In Δ APQ and Δ ABC
∠APQ ≅ ∠ACB {Corresponding angles are equal since PQ is parallel to BC}
∠A≅ ∠A ……….....{Reflexive Property}
Δ APQ~ Δ ABC….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
[tex]\dfrac{AP}{AB} =\dfrac{AQ}{AC}=\dfrac{PQ}{BC} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
Substituting the values we get
[tex]\dfrac{AP}{AB} =\dfrac{AQ}{AC}\\\\\dfrac{20}{36} =\dfrac{5x}{45}\\\\x=\dfrac{20\times 45}{36\times 5}=5\\\\x=5[/tex]
Therefore the value of x is
[tex]x=5[/tex]
