Answer:
The first x = 4
The second x = 6.25
Step-by-step explanation:
For the first question. We need to make use of the midsegment theorem which says, if you have a trapezoid with base1 and base2, then the midsegment is given as:
(Base1 + Base 2)/2.
We are given Base 1 = 5x + 3 and Base 2 = 12x – 3 and the midsegment, JK = 34. To find x we have:
(5x + 3 + 12x – 3)/2 = 34
This gives: 17x/2 = 34.
Therefore, x = (34 x 2)/17 = 4. Thus, x = 4.
As for the second question, we have two diagonals of the rectangle, FH and JG. We are given that JG = 40. We know that the diagonals of the rectangle are equal, therefore FH = 40 as well.
We are told that M is the midpoint, meaning FM is half of the diagonal FH. Mathematically this can be written as:
FM = FH/2
Given that FM = 3.2x and FH = 40, we have:
3.2x = 40/2
3.2x = 20
x = 20/3.2
x = 6.25
