a rectangular 10 t measures 54 meters in perimeter and 180 square meters in area. what are its length and width respectively?
To find the dimensions of the rectangle, we can use the given information about its perimeter and area.
Let's assume the length of the rectangle is L and the width is W.
We know that the perimeter of a rectangle is calculated by adding the lengths of all four sides. So, for this rectangle, the perimeter equation is given as:
2L + 2W = 54 (since there are two lengths and two widths)
Now, we have another equation based on the area of the rectangle. The area of a rectangle is calculated by multiplying its length and width. So, the area equation is:
L * W = 180
We now have a system of two equations with two variables (L and W). We can solve this system to find the values of L (length) and W (width).
Let's start by rearranging the perimeter equation to solve for L:
2L + 2W = 54
2L = 54 - 2W
L = (54 - 2W) / 2
L = 27 - W
Now, substitute this value of L in the area equation:
(27 - W) * W = 180
27W - W^2 = 180
Rearrange the equation:
W^2 - 27W + 180 = 0
Now, this is a quadratic equation that can be factored:
(W - 12)(W - 15) = 0
Therefore, W = 12 or W = 15
Plugging these values back into the perimeter equation will give us the corresponding values of L:
If W = 12:
L = 27 - 12 = 15
If W = 15:
L = 27 - 15 = 12
So, the possible dimensions of the rectangle are length = 15 meters and width = 12 meters.