PSAT Math Multiple-Choice Question 446: Answer and Explanation

Question: 446

A rectangle has an area of If the width of the rectangle is , what is the length?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

B

Difficulty: Medium

Getting to the Answer: Start by noticing that the area equation is a difference of perfect squares. Use the difference of squares formula (a² - b²) = (a + b)(a - b) where (x⁴ - 196) = (x² + 14)(x² - 14). Because area is length times width (A = lw) and the width is x² - 14, the length must be x² + 14, so (B) is correct.