Question

In trapezoid PQRS, if segment XY is the midsegment, which could be the lengths PQ and SR? Select all that apply.

17 cm and 31 cm
18 m and 30 m
4 cm and 8 cm
9 cm and 15 cm
12 cm and 36 cm
18 cm and 30 cm

please explain how you get the answer :)​

Answer 1

17 cm and 31 cm

12 cm and 36 cm

18 cm and 30 cm

Explanation:

The midsegment of a trapezoid is equal to the average of the two bases. When taking an average of two numbers, you add them and divide by 2. So the equation will be as follows:

`(PQ + SR)/(2) = XY`

XY is given to be 24, so:

`(PQ + SR)/(2) = 24`

Multiplying on both sides gets us:

`PQ + SR = 48`

So any values of PQ and SR that add to 48 work. Therefore, we will sum the given options:

17 cm + 31 cm = 48 cm

18 m + 30 m = 48m (Did you mean meters?)

4 cm + 8 cm = 12cm

9 cm + 15 cm = 24cm

12 cm + 36 cm = 48cm

18 cm + 30 cm = 48 cm