The length of a rectangle is 6 units and its width is 4 units. What is the approximate length of the diagonal of the rectangle? (5 points)
2 units
4.4 units
6 units
7.2 units
To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the diagonal is the hypotenuse, and the length and width of the rectangle are the other two sides.
Using the Pythagorean theorem, we can calculate the length of the diagonal as follows:
diagonal^2 = length^2 + width^2
diagonal^2 = 6^2 + 4^2
diagonal^2 = 36 + 16
diagonal^2 = 52
Taking the square root of both sides, we find:
diagonal ≈ √52
Now, let's estimate the square root of 52. The perfect squares that are closest to 52 are 49 (7^2) and 64 (8^2). Since the square root of 52 is between 7 and 8, we can estimate it to be around 7.2 units.
Therefore, the approximate length of the diagonal of the rectangle is 7.2 units.
Answer: 7.2 units.