Question

Given the median line QR and trapezoid MNOP, what is the value of x? MN=17 QR=x+12 OP=5x-14

Answer 1

x = 7.

The person that answered is correct, if you got the answer wrong that means you didn't look hard enough for the answer in their answer.

Answer 2

Answer:
x = 7
MN (first base) = 17 units
OP (second base) = 21 units
QR (median) = 19 units

Step-by-step explanation:
In a trapezium, the length of the median is equal to half the sum of the two bases.

From the given, we have:
MN (first base) = 17 units
OP (second base) = 5x - 14 units
QR (median) = x + 12 units

Applying the above rule:
median = 0.5 (first base + second base)
x + 12 = 0.5 (17+5x-14)
2(x+12) = 17+5x-14
2x + 24 = 3 + 5x
24-3 = 5x-2x
21 = 3x
x =
`(21)/(3)`
x = 7

Based on the above, the lengths would be:
MN (first base) = 17 units
OP (second base) = 5x - 14 = 5(7) - 14 = 21 units
QR (median) = x + 12 = 7 + 12 = 19 units

Hope this helps :)