Question

15 fill in the blank 1 point

1. find rs.

r 2x + 15 s
v 3x + 5 w
u 6x - 37 i

Explanation:

Step1: Set up midsegment theorem equation

The segment VW is the midsegment of trapezoid RSTU, so it equals the average of RS and UT.
$$3x - 5 = \frac{(2x + 15) + (6x - 37)}{2}$$

Step2: Simplify the right-hand side

Combine like terms in the numerator.
$$3x - 5 = \frac{8x - 22}{2}$$
$$3x - 5 = 4x - 11$$

Step3: Solve for x

Isolate x by subtracting 3x and adding 11.
$$-5 + 11 = 4x - 3x$$
$$x = 6$$

Step4: Calculate RS

Substitute x=6 into the expression for RS.
$$RS = 2(6) + 15$$

Answer:

37