Multiple choice

Directions: The following problem has a question and two statements labelled (A) and (B). Use the data given in (A) and (B) to decide whether the statements are sufficient to answer the question. What is its perimeter if the area of a rectangle is 20? (A) The length of the rectangle is 5. (B) The width of the rectangle is 1 unit less than its length.

  1. If the question can be solved using statement (A) alone

  2. If the question can be solved using either or both of the statements

  3. If the question can be solved using statement (B) alone

  4. If the question cannot be solved using the given statements
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area = L * W = 20. (A) L = 5 implies W = 4. Perimeter = 2(5+4) = 18. (B) W = L - 1 implies L(L-1) = 20, which is a quadratic equation L^2 - L - 20 = 0, solving for L gives 5, so W=4. Both statements alone are sufficient.

AI explanation

Using statement A, if the length is 5 and the area is 20, the width is 20 divided by 5, which equals 4, and the perimeter is 2 times (5 + 4) or 18. Using statement B, if the area is 20 and the width is L minus 1, the equation L(L - 1) = 20 yields L = 5, again giving a width of 4 and a perimeter of 18. The question can be solved using either statement alone.

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