Respuesta :
Answer:
5 cm by 5 cm
Step-by-step explanation:
The perimeter of this rectangle is 20 cm, and the relevant formula is
P = 20 cm = 2W + 2L. Then W + L = 10 cm, or W = (10 cm) - L.
The area of the rectangle is A = L·W, and is to be maximized. Subbing (10 cm) - L for W, we get A = L[ (10 cm) - L ], or A = 10L - L²
Note that this is the equation of a parabola that opens down. With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is
x = -b / (2a). Subbing 10 for b and -1 for a, we get:
x = -[10] / [2·(-1)] = 10/2, or 5.
This tells us that one dimension of the rectangle is 5 cm.
Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:
20 cm = 2(5 cm) + 2W, or
10 cm = W + 5 cm, or W = 5 cm.
Thus, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.
The dimensions that give the maximum area is 5 cm by 5 cm.
Given:
The perimeter of this rectangle is 20 cm, and formula for perimeter is
P= 2(W+L)
P = 20 cm = 2W + 2L.
Then W + L = 10 cm,
or W = (10 cm) - L.
The area of the rectangle is A = L·W, and is to be maximized.
On substituting the values, we get A = L[ (10 cm) - L ], or A = 10L - L²
Note that this is the equation of a parabola that opens down. With coefficients a = -1, b = 10 and C = 0, we find that the x-coordinate of the vertex (which is the x-coordinate of the maximum as well) is
x = -b / (2a). Subbing 10 for b and -1 for a, we get:
x = -[10] / [2·(-1)] = 10/2, or 5.
This tells us that one dimension of the rectangle is 5 cm.
Since P = 20 cm = 2L + 2W, and if we let L = 5 cm, we get:
20 cm = 2(5 cm) + 2W, or
10 cm = W + 5 cm, or W = 5 cm.
Therefore, choosing L = 5 cm and W = 5 cm results in a square, which in turn leads to the rectangle having the maximum possible area.
Learn more:
brainly.com/question/24639460
