The value of x is 11
Explanation:
Given that UVW and STU are similar triangles.
Also, given that [tex]UV=5x+11[/tex], [tex]VW=88[/tex], [tex]SU=18[/tex] and [tex]ST=24[/tex]
The value of x:
For similar triangles, their sides will be proportional.
Hence, we have,
[tex]\frac{UV}{SU}=\frac{VW}{ST}[/tex]
Substituting the values, we get,
[tex]\frac{5 x+11}{18}=\frac{88}{24}[/tex]
Let us multiply both sides by 18, we get,
[tex]5 x+11=\frac{88(18)}{24}[/tex]
Multiplying the terms in the numerator, we get,
[tex]5 x+11=\frac{1584}{24}[/tex]
Dividing the terms, we have,
[tex]5 x+11=66[/tex]
Subtracting both sides by 11, we get,
[tex]5 x=55[/tex]
Dividing both sides by 5, we have,
[tex]x=11[/tex]
Hence, the value of x is 11
