Digital PSAT Math Practice Question 277: Answer and Explanation

Question: 277

If a square has a diagonal that measures units, what is the square's perimeter in units?

Correct Answer: 12

Explanation:

12 A diagonal of a square cuts that square into two 45-45-90 triangles. If the diagonal of the square (the hypotenuse of the triangles) has a length of then that square will have side lengths of 3. This is because a 45-45-90 triangle has legs of length x and a hypotenuse of length (This relationship is given on the formula sheet at provided in the math section).

Therefore, the perimeter of the square will be 4l = 4(3) = 12.

Alternatively, if you don't recognize this special triangle, you know that this is a square, so the two sides of the triangle will have the same length l. Using the Pythagorean theorem, . Dividing by 2 gives l² = 9, so l = 3.