Question:
In the following figure, if DE || BC, then x =
In the following figure, if DE || BC, then x =
Updated On: Apr 29, 2025
- \(\sqrt 3\)
- \(\sqrt 7\)
- \(\sqrt 6\)
- \(\sqrt 5\)
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The Correct Option is B
Solution and Explanation
Since DE is parallel to BC, the BPT states that the ratio of corresponding sides is equal.
Therefore: AD/AB = AE/AC = DE/BC
Substitute the given values: (x + 4) / (x + 4 + x + 3) = (2x - 1) / (2x - 1 + x + 1)
Simplify: (x + 4) / (2x + 7) = (2x - 1) / (3x)
Cross-multiply: 3x(x + 4) = (2x + 7)(2x - 1)
Expand: 3x² + 12x = 4x² + 12x - 7
Solve for x:** 0 = x² - 7 x² = 7 x = √7
So, the correct answer is (2) √7.
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