Multiple choice

Solve the equation obtained $x^{2} - x - 6 = 0$ and hence find the dimensions of the verandah. Verandah is in rectangular shape having area and perimeter equal.

  1. x = 3; length = 6 m and breadth = 3 m

  2. x = 3; length = 6 m and breadth = 4 m

  3. x = 3; length = 4 m and breadth = 3 m

  4. x = 4; length = 6 m and breadth = 3 m
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A Correct answer
Explanation

x^2 - x - 6 = 0 => (x-3)(x+2) = 0. x=3. Area = L*B, Perimeter = 2(L+B). If L=6, B=3, Area = 18, Perimeter = 2(9) = 18. Matches.

AI explanation

Factoring the quadratic equation x^2 - x - 6 = 0 yields (x - 3)(x + 2) = 0, giving the positive solution x = 3. A rectangular verandah having equal area and perimeter satisfies the equation length * breadth = 2(length + breadth). Substituting the value x = 3 into the dimensions 2x and x results in a length of 6 m and a breadth of 3 m, since 6 * 3 = 18 and 2(6 + 3) = 18. Therefore, the dimensions are x = 3; length = 6 m and breadth = 3 m.

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