Given:
Given that the bases of the trapezoid are 21 and 27.
The midsegment of the trapezoid is 5x - 1.
We need to determine the value of x.
Value of x:
The value of x can be determined using the trapezoid midsegment theorem.
Applying the theorem, we have;
[tex]Midsegment = \frac{b_1+b_2}{2}[/tex]
where b₁ and b₂ are the bases of the trapezoid.
Substituting Midsegment = 5x - 1, b₁ = 21 and b₂ = 27, we get;
[tex]5x-1=\frac{21+27}{2}[/tex]
Multiplying both sides of the equation by 2, we have;
[tex]2(5x-1)=(21+27)[/tex]
Simplifying, we have;
[tex]10x-2=48[/tex]
Adding both sides of the equation by 2, we get;
[tex]10x=50[/tex]
Dividing both sides of the equation by 10, we have;
[tex]x=5[/tex]
Thus, the value of x is 5.
