So here is my question,

"The area of trapezoid PQRS is 60. One base is 7 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of trapezoid PQRS."

I have read another thread on this website with a similar question

https://web2.0calc.com/questions/the-area-of-trapezoid-abcd-is-60-one-base-is-4-units-longer-than-the-other-and-the-height-of-the-trapezoid-is-5-find-the-length-of-the-median-of-the

I followed the steps that CPhill and Melody have given changing the numbers to fit my question but I have no idea how u get the other parrell side length.

Here is my work so far using CPhill's method

60 = 5/2 * (x+x+7)

60*(2/5)= 2x + 7

24 = 2x + 7

17 = 2x

x=8.5

How do I find the other parell side? Once you have the parell side can't you just find the average of the parell sides like CPhill and Melody did?

Thank you in advance I know this is a lengthy quesiton :D

Guest May 8, 2020

#1**+1 **

Based on Melody's post in the question you linked, yes, you can find the median by averaging the two parallel sides. It seems like you're having trouble finding the parallel sides.

Call one parallel side x and the other x+7

The area of the trapezoid is the sum of the parallel sides times the height divided by 2 which equals 60 in this case.

\(\frac{h(b_1+b_2)}{2}\)

Since we know the height and the area, we can solve for the sides.

\(\frac{5(x+x+7)}{2}=\frac{10x+35}{2}=60\) From this, we get x=8.5. So we know your work above is correct. Since 1 side is x and the other is x+7, the two parallel sides are **8.5 and 15.5**. To find the median, take the average of these two numbers.

HELPMEEEEEEEEEEEEE May 8, 2020