The area of the triangle described will be √231 cm^2 ≈ 15.20 cm^2. The height will be computed from
area = (1/2)*(base)*(height)
2*area/base = height
2*(15.20 cm^2)/(10 cm) = 3.04 cm = height
A triangle with a base of 10 cm and an area of 16 cm^2 will have a height of
2*(16 cm^2)/(10 cm) = 3.2 cm, corresponding to choice (c).
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area = (1/2)*(base)*(height)
2*area/base = height
2*(15.20 cm^2)/(10 cm) = 3.04 cm = height
A triangle with a base of 10 cm and an area of 16 cm^2 will have a height of
2*(16 cm^2)/(10 cm) = 3.2 cm, corresponding to choice (c).
_____
Your math text is in error as often as not, apparently. Please lobby for a new one.