Answer:
The correct option is 4.8 units
Step-by-step explanation:
Look at the attached picture.
AB = 8.6
Coordinates of A(1, 3), B(8, 8), C(12, 5) and D(5, 0)
Now find the angle between AB and AD to find the length of AE which is the length of parallelogram.
tanθ = m(AB)-m(AD)/1+m(AB)m(AD)
Slope of mAB = y2-y1/x2-x1
Slope of mAB = 8-3/8-1
Slope of mAB = 5/7
Slope of mAD = 0-3/5-1 = -3/4
tanθ = 5/7 - (-3/4)/ 1+(5/7)(-3/4)
tanθ = 5/7+3/4 / 1+(-15/28)
tanθ = 20+21/28 /1 - 15/28
tanθ = 41/28 / 28-15/28
tanθ = 41/28 /13/28
Both the denominators will be cancelled out by each other.
tanθ = 41/13 = 3.154
θ = tan^-1 (3.154) = 72.41 degree
Now in right angle triangle ABE
sin72.41° = DE/5
.95324 = DE/5
DE = 5×4.7662 = 4.8 units
Thus the correct option is 4.8 units
