The length of a rectangle is 6 meters longer than the width. If the area is 25 square meters, find the rectangle’s dimensions. Round to the nearest tenth of a meter.
Let's say the width of the rectangle is x meters.
The length of the rectangle is then (x+6) meters.
The area of the rectangle is given by length * width, so:
x(x+6) = 25
x^2 + 6x = 25
x^2 + 6x - 25 = 0
Using the quadratic formula, we obtain:
x = (-b ± √(b^2-4ac))/(2a)
x = (-6 ± √(6^2-4*1*(-25)))/(2*1)
x = (-6 ± √(36+100))/2
x = (-6 ± √(136))/2
x = (-6 ± 11.66)/2
So x could be either:
x = (-6 + 11.66)/2 = 2.83
or
x = (-6 - 11.66)/2 = -8.83 (discarding the negative solution since we are dealing with dimensions)
Therefore, the width of the rectangle is approximately 2.83 meters and the length is approximately (2.83 + 6) = 8.83 meters.