Question

5 fill in the blank 2 points
gr.1.5
trapezoid pqrs is shown. find yz.
$pq=38$
$yz=5x-19$
$sr=x+14$
$yz=$ type your answer... units

Explanation:

Step1: Apply trapezoid midsegment theorem

The midsegment of a trapezoid is the average of the two bases, so:
$$5x - 19 = \frac{38 + (x + 14)}{2}$$

Step2: Simplify right-hand side

Combine terms in the numerator, then divide:
$$5x - 19 = \frac{x + 52}{2}$$

Step3: Eliminate denominator

Multiply both sides by 2:
$$10x - 38 = x + 52$$

Step4: Isolate x terms

Subtract $x$ from both sides:
$$9x - 38 = 52$$

Step5: Solve for x

Add 38 to both sides, then divide by 9:
$$9x = 90 \implies x = 10$$

Step6: Calculate YZ

Substitute $x=10$ into $5x-19$:
$$YZ = 5(10) - 19$$

Answer:

31 units