Final answer:
Using the Pythagorean theorem, the length of the diagonal of the rectangle with adjacent vertices (-1,2) and (6,2) and side lengths of 3 units is approximately 7.6 units.
Step-by-step explanation:
To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem which states that in a right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse. The given points (-1,2) and (6,2) are adjacent vertices of a rectangle, and they form one side of the rectangle. Since both these points have the same y-coordinate, this side is horizontal, and its length can be calculated by taking the difference of the x-coordinates: 6 - (-1) = 7 units.
Since two sides of the rectangle have a length of 3 units, and these represent the shorter sides of the rectangle, we can form a right triangle where one side is 3 units (the width), another side is 7 units (the length), and the diagonal of the rectangle is the hypotenuse. Applying the Pythagorean theorem:
√(3 units)² + (7 units)² = √(9 units² + 49 units²) = √58 units²
To the nearest tenth, the diagonal is approximately:
√58 units² ≈ 7.6 units
Therefore, the answer to the length of the diagonal of the rectangle is 7.6 units.