Given:
[tex]\Delta UVW\sim \Delta USR[/tex]
To find:
The missing length marked with a question mark.
Solution:
Let x be the missing value.
We have,
[tex]\Delta UVW\sim \Delta USR[/tex]
Corresponding sides of similar triangles are proportional, so
[tex]\dfrac{UV}{US}=\dfrac{VW}{SR}=\dfrac{UW}{UR}[/tex]
Using this, we get
[tex]\dfrac{UV}{US}=\dfrac{UW}{UR}[/tex]
On substituting the values, we get
[tex]\dfrac{70}{x}=\dfrac{55}{44}[/tex]
[tex]\dfrac{70}{x}=\dfrac{5}{4}[/tex]
On cross multiplication, we get
[tex]70\times 4=5\times x[/tex]
[tex]280=5x[/tex]
[tex]\dfrac{280}{5}=x[/tex]
[tex]56=x[/tex]
Therefore, the missing length is 56 units.
