Final answer:
Dimensions of the rectangle are 4 meters by 12 meters.
Step-by-step explanation:
To find the dimensions of the rectangle, let's assume that the shorter side of the rectangle is 'x' meters. According to the problem, the diagonal of the rectangle is 8 meters longer than its shorter side, so the diagonal would be 'x + 8' meters. We know that the area of a rectangle is given by length times width, so we can set up the equation 'x * (x+8) = 60' to represent the area of the rectangle. Solving this equation will give us the dimensions of the rectangle.
Multiplying x and x+8, we get x^2 + 8x = 60. Rearranging the equation, we have x^2 + 8x - 60 = 0. Factoring the quadratic equation, we find (x - 4)(x + 12) = 0. This means that either x - 4 = 0 or x + 12 = 0. Solving for x, we get x = 4 or x = -12. Since we are dealing with dimensions, we discard the negative value of x, so the shorter side of the rectangle is 4 meters.
Now we can find the longer side of the rectangle by adding 8 meters to the shorter side. Adding 8 to 4, we get 12. So the dimensions of the rectangle are 4 meters by 12 meters.