Final answer:
To estimate each dimension of the rectangle to the nearest meter, we first set up and solve the quadratic equation x² + 2x = 70. Upon finding the value of x, we also calculate x+2. Both values are then rounded to the nearest whole meter.
Step-by-step explanation:
The problem given is a quadratic equation where the area of the rectangle is 70 m², and the length (L) and width (W) are represented by x and x+2 respectively. To solve for x, we use the formula for the area of a rectangle, which is L × W. Substituting the given expressions in terms of x, we have:
x(x+2) = 70
Expanding this, it becomes:
x² + 2x = 70
To find the value of x, we need to solve this quadratic equation. We rearrange it into standard form:
x² + 2x - 70 = 0
Using the quadratic formula, x can be found as:
x = [-b ± √(b²-4ac)] / (2a)
Where a = 1, b = 2, and c = -70. Plugging in these values, we get two solutions for x. We reject the negative solution since a length can't be negative, and accept the positive one. Once we find x, we can also find x+2 to get both dimensions of the rectangle. The values are then rounded to the nearest meter as requested.