ABCD is a rectangle. What is the value of x? (1 point)
rectangle with length 63 m, width x m, and diagonal 65 m
2 meters
16 meters
63 meters
65 meters
To find the value of x, we can use the Pythagorean theorem since ABCD is a rectangle. The theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides.
In this case, the diagonal is 65 m, and the two other sides are the length, 63 m, and the width, x m. Therefore, we can write the equation as:
65^2 = 63^2 + x^2
4225 = 3969 + x^2
256 = x^2
Taking the square root of both sides, we get:
x = ± 16
Since the width of a rectangle cannot be negative, the value of x is 16 meters.
Therefore, the correct answer is:
16 meters