can someone please just set the equation for me to solve this problem . thanks
A solar collector is 2.5m long by 2.0m wide. It is held in place by a frame of uniform width around its outside edge. If the exposed collector area is 2.5m^2, what is the width of the frame, to the nearest tenth of a centimeter?
The area of the collector is (2.5-w)(2.0-w). Set that equal to 2.5, and solve for w.
To solve this problem, we need to set up an equation using the given information.
Let's assume that the width of the frame is "w" (in meters). The total length of the solar collector, including the frame, would be 2.5 + 2w meters, and the total width would be 2 + 2w meters.
The area of the collector (including the frame) is the product of the length and width, which will be equal to 2.5 square meters:
(2.5 + 2w)(2 + 2w) = 2.5
Now, let's expand the equation:
5 + 5w + 4w + 4w^2 = 2.5
Combining like terms and moving all terms to one side, we get:
4w^2 + 9w + 2.5 - 5 = 0
Simplifying further:
4w^2 + 9w - 2.5 = 0
Now we have a quadratic equation which we can solve using various methods such as factoring, completing the square, or the quadratic formula.
Once we find the values of "w" that satisfy this equation, we can round the solution to the nearest tenth of a centimeter to find the width of the frame.