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 = (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=(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.