Final answer:
To find the measure of bar (DE), we set the given expressions for GH and DE equal to each other since DE is the midpoint. By solving for x and then substituting back into the expression for DE, we find that the measure of bar (DE) is approximately 31.25.
Step-by-step explanation:
To find the measure of bar (DE), we are given that GH = 22 + 3x and DE = -9x + 59. Because DE is the midpoint of EF, GH should also be equal to DE, making their expressions equal to each other.
We set the expressions for GH and DE equal to solve for x:
22 + 3x = -9x + 59.
To isolate x, we first add 9x to both sides of the equation:
22 + 3x + 9x = -9x + 9x + 59
22 + 12x = 59.
Next, subtract 22 from both sides:
12x = 59 - 22
12x = 37.
Finally, divide by 12 to get the value of x:
12x/12 = 37/12
x = 37/12
x = 3.0833 (approximately).
Plug this value back into the expression for DE to get its measure:
DE = -9x + 59
DE = -9(3.0833) + 59
DE = -27.75 + 59
DE = 31.25 (approximately).
Therefore, the measure of bar (DE) is approximately 31.25.