## UnicornPoopCookies 3 years ago Given the median and trapezoid MNOP, what is the value of x? (Picture included)

2. nincompoop

what do you know about trapezoids?

Well i know it has two pairs of parallel sides.

4. nincompoop

if you are able to prove that QM and QN are congruent, and RP and RO are congruent, then you would be able to prove that the figure is trapezoid $QR=\frac{ 1 }{ 2 }(MP+NO)$

5. nincompoop

let us try to solve for the x

6. nincompoop

what should we do to get the value of x? I provided the equation for the medial of trapezoid for you to use to find the value of x. I prefer that you participate in solving and not be a spectator.

7. nincompoop

do you want to do this together or what @UnicornPoopCookies

I got 12?

9. nincompoop

10. nincompoop

hello @unicornpoopcookies the answer IS NOT 12 show how you got 12

11. nincompoop

QR = 1/2(MP+NO) x+15 = 1/2 [(9x -42) + 30] // perform the operation in the parentheses x+15 = 1/2 (9x -12) //to make our problem easier by multiply both sides by 2. this will cancel out 1/2 and 2 and will give us: 2 (x+15) = 9x - 12 // distributive property on left hand side (LHS) of the equation 2x + 30 = 9x - 12 // isolate terms, our x, into the LHS by subtracting -9x on both sides of the equation. this will give us 2x -9x + 30 = 9x - 9x -12 // perform the operation. -7x + 30 = -12 // continue to isolate our x by subtracting 30 on both sides of the equation. this will give us: -7x + 30 - 30 = -12 - 30 // perform the operation -7x = -42 // look for the value of x by dividing both sides of the equation by -7 x = 6