Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryEasy
A construction worker is laying a rectangular concrete slab that needs to be 12 feet long and 9 feet wide. To ensure the slab is perfectly rectangular, the worker must verify that the diagonals are equal in length. What is the length of one diagonal?
- A25 feet
- B10 feet
- C21 feet
- D15 feet
Show answer & explanationAnswer & explanation
Correct answer: D. 15 feet
The diagonal of a rectangle forms a right-angled triangle with two adjacent sides. The length of the diagonal can be found using the Pythagorean theorem, where the sides of the rectangle are the legs (a and b) and the diagonal is the hypotenuse (c).
Why the other options are wrong
- A. This is incorrect; it might result from a miscalculation of the square root or an incorrect formula.
- B. This is incorrect; it might result from an incorrect calculation or formula.
- C. This is incorrect; it might be the sum of the length and width, not the diagonal.
Diagonal of a Rectangle
A line segment connecting two non-adjacent vertices of a rectangle, dividing it into two congruent right-angled triangles.
- The diagonals of a rectangle are equal in length.
- The diagonal forms the hypotenuse of a right triangle with the sides of the rectangle.
- Its length can be calculated using the Pythagorean theorem.
Memory trick: Remember, a rectangle's diagonal 'cuts' it into two 'right' triangles!