PSAT Math Grid-Ins Question 18: Answer and Explanation

Question: 18

The diagonal of rectangle ABCD is 13 inches long. What is the area of rectangle ABCD?

Correct Answer: 60

Explanation:

60

The question asks for the area of rectangle ABCD. Use the geometry basic approach. Start by labeling the figure with the given information. The length of one side is 5, and the question states that the length of the diagonal, BD (or AC), is 13. The formula for the area of a rectangle is A = (length) (width), so find the width first. Since the corner of the rectangle is a right angle, use the Pythagorean Theorem: a² + b² = c². Plug in AB for a and BD for c so that 5² + b² = 13². Then solve for b, which will be AD, the length of the other side of the right triangle, and thus the width of the rectangle. First, simplify: 25 + b² = 169. Then subtract 25 from both sides and take the square root: . Then, b = 12. Since AD = 12, plug the length and width into the formula for the area of a rectangle to get A = (5)(12) = 60. The correct answer is 60.