Straight Lines
Grade None
Question:
<p>The two adjacent sides of a parallelogram are given by 2x<sup>2</sup> + 2y<sup>2</sup> - 5xy = 0 and 5x + 2y = 1 is one of its diagonal. If area of parallelogram is S, then <span class="math-tex">\(\sqrt{S}\)</span> is equal to :</p>
<p style="display:inline"><span class="math-tex">\(\frac{1}{6}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{2}{3}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{1}{2}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{3}{4}\)</span></p>
Step-by-Step Solution
Key Concept: Factor the pair of lines to identify the two adjacent sides and calculate the area of the parallelogram as twice the area of the triangle formed by these sides and the given diagonal.
<p><span class="math-tex">\(\frac{1}{6}\)</span></p>
Correct Answer: A