Final answer:
The length of the other parallel side LM in trapezoid LMNO is calculated using the trapezoid area formula. It is determined to be 6 cm, which corresponds to option b.
Step-by-step explanation:
To find the length of the other parallel side, LM, in trapezoid LMNO with an area of 21 cm² and a height of 3 cm, where one parallel side, ON, is 8 cm long, we use the formula for the area of a trapezoid:
A = (1/2) * h * (a + b), where A is the area, h is the height, a and b are the lengths of the parallel sides.
We can rearrange this formula to solve for b (the unknown side length LM):
b = (2A/h) - a.
Plugging in the known values gives us:
b = (2 * 21 cm² / 3 cm) - 8 cm
= 14 cm - 8 cm
= 6 cm.
So, the length of side LM is 6 cm, which means the correct answer is b. LM = 6 cm.