Question

determine the following values *
xztp is a trapezoid where xp || zt. sl is a midsegment of xztp and xs = 7, lt = 6, sl = 10, tz = 2x - 4, and xp = x - 3.
(there is an image of trapezoid xztp with sl as a midsegment, and a table with numbers 3, 6, 9, 12, 14, 16, 18, 20 and checkboxes for x=, xp=, zt=)

Explanation:

Step1: Apply midsegment theorem

The midsegment of a trapezoid is equal to half the sum of the two parallel sides, so:
$$SL = \frac{XP + ZT}{2}$$

Step2: Substitute given values

Plug in $SL=10$, $XP=x-3$, $ZT=2x-4$:
$$10 = \frac{(x-3) + (2x-4)}{2}$$

Step3: Simplify and solve for x

Multiply both sides by 2, then combine like terms:
$$20 = 3x - 7$$
$$3x = 27$$
$$x = 9$$

Step4: Calculate XP

Substitute $x=9$ into $XP=x-3$:
$$XP = 9 - 3 = 6$$

Step5: Calculate ZT

Substitute $x=9$ into $ZT=2x-4$:
$$ZT = 2(9) - 4 = 14$$

Answer:

$x = 9$
$XP = 6$
$ZT = 14$