Parallelogram Height 287Ac7

1. **State the problem:** We have a parallelogram with area $12$ square units. One side length is $18$ units, the other side length is $6$ units. We need to determine if given dimensions can be the height corresponding to either side. 2. **Formula for area of a parallelogram:** $$\text{Area} = \text{base} \times \text{height}$$ 3. **Check heights for each side:** - For base $18$ units, height $h$ satisfies: $$12 = 18 \times h \implies h = \frac{12}{18} = \frac{2}{3}$$ - For base $6$ units, height $h$ satisfies: $$12 = 6 \times h \implies h = \frac{12}{6} = 2$$ 4. **Evaluate each given height:** - $\frac{2}{3}$ unit: This matches height for base $18$, so height $= \frac{2}{3}$ is possible. But user says No, so let's check carefully. Since the height must be perpendicular to the base, the height corresponding to base $18$ is $\frac{2}{3}$. - $\frac{3}{2} = 1.5$ units: Check if this can be height for either base. For base $18$, height $1.5$ gives area $18 \times 1.5 = 27 \neq 12$. For base $6$, height $1.5$ gives area $6 \times 1.5 = 9 \neq 12$. So $1.5$ units is not a valid height. - $2$ units: For base $6$, height $2$ gives area $6 \times 2 = 12$, valid. - $3$ units: For base $18$, height $3$ gives area $18 \times 3 = 54 \neq 12$. For base $6$, height $3$ gives area $6 \times 3 = 18 \neq 12$. So $3$ units is not a valid height. 5. **Conclusion:** - $\frac{2}{3}$ unit: Yes (height for base $18$) - $\frac{3}{2}$ units: No - $2$ units: Yes (height for base $6$) - $3$ units: No **Note:** The user states $\frac{2}{3}$ unit — No and $3$ units — Yes, which contradicts the area formula. The correct answers based on the formula are: $\frac{2}{3}$ unit — Yes $\frac{3}{2}$ units — No $2$ units — Yes $3$ units — No