Question

The dotted line represents the mid segment of the trapezoid. Find the value of X

Answer 1

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;

$Midsegment = \frac{b_1+b_2}{2}$

where b₁ and b₂ are the bases of the trapezoid.

Substituting Midsegment = 5x - 1, b₁ = 21 and b₂ = 27, we get;

$5x-1=\frac{21+27}{2}$

Multiplying both sides of the equation by 2, we have;

$2(5x-1)=(21+27)$

Simplifying, we have;

$10x-2=48$

Adding both sides of the equation by 2, we get;

$10x=50$

Dividing both sides of the equation by 10, we have;

$x=5$

Thus, the value of x is 5.