Straight Lines
Straight Lines
nta_abhyas_2025
Grade 11
Question:
If a parallelogram $ABCD$ is as shown in the figure. Let the distance between $AB$ & $CD$ is $d_1$, and the distance between $AD$ & $BC$ is $d_2$, and $\angle DAD = \angle DCB = \theta$ then
Step-by-Step Solution
Key Concept: Using the relationship between distances between parallel sides and side lengths through trigonometry
Setting up the parallelogram with the given constraints, we have $AD = d_1 \cos\theta$ and $DC = d_1 \cos\theta$. The perimeter of parallelogram $ABCD$ is $2(AD + DC) = 2\left(\frac{1+3}{2} + \frac{15-1}{8}\right) = 2\left(2 + 2\right) = 2\left(\frac{5}{2} + \frac{5}{2}\right) = 5 + 5 = 5\sqrt{5}$.
Correct Answer: 5