Se desea cortar una tela en pedazos rectangulares cuya área sea igual a 72 cm2 a. Elaborar la tabla que muestra los posibles valores para el largo y el ancho de los rectángulos. b. Determinar la relación entre el largo, l, y el ancho, a, de los rectángulos. c. Determinar la expresión matemática que relaciona el largo y el ancho. d. Realizar la gráfica que representa los valores del largo y el ancho

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the mathematical expression that relates the length and width:

y = 72/x

See explanation and attachments below for other answers to the question.

Question:

You want to cut a fabric into rectangular pieces whose area is equal to 72 cm2

a. Prepare the table that shows the possible values ​​for the length and width of the rectangles.

b. Determine the relationship between the length, l, and the width, a, of the rectangles.

c. Determine the mathematical expression that relates the length and width.

d. Make the graph that represents the values ​​of the length and width.

Explanation:

a) Area of the rectangle = 72cm²

Area of a rectangle = length × breadth = l×b

Let's find the factors of 72:

1,2,3,4,6,8,9,12,18,24,36,72

Since length is longer than width, the length would have the longest side in each possible dimension.

Possible dimensions of the rectangles (width ×length):

1×72; 2×36; 3×24; 4×18; 6×12; 8×9

See the attachment for the table that shows the possible values ​​for the length and width of the rectangle.

Let y = length and x= width

b) The relationship between the length, l, and the width, w, of the rectangles:

Area = l × w

72 = lw

l = 72/w

The relationship between the length, l, and the width, w, of the rectangles: l = 72/w

c) Area = x × y

Since y = length and x= width

72 = xy

y = 72/x

the mathematical expression that relates the length and width:

y = 72/x

d) see attachment for the graph