Question

Cuanto mide el largo de un rectángulo cuyo perímetro es 16cm y su área 12 cm al cuadrado ?

Answer 1

To find the length of a rectangle given its perimeter and area, use the formulas for perimeter and area. In this case, the length of the rectangle is 6 cm.

Step-by-step explanation:

To find the length of a rectangle given its perimeter and area, we can use the formulas:

Perimeter = 2(length + width)

Area = length * width

In this case, the perimeter is given as 16 cm and the area is given as 12 cm2. Let's solve:

16 = 2(length + width)

12 = length * width

From the first equation, we can simplify it to:

8 = length + width

Now we can solve the equations simultaneously:

width = 8 - length

12 = length * (8 - length)

12 = 8length - length2

Now rearrange the equation:

length2 - 8length + 12 = 0

Factor the quadratic equation:

(length - 6)(length - 2) = 0

From the equation, we can see that length = 6 or length = 2. Since the rectangle cannot have a length of 2 cm (as it would not be larger than its width), the length of the rectangle is 6 cm.

Answer 2

Hay dos rectángulos posibles que satisfacen las condiciones dadas: uno de 2 cm de largo y 6 cm de ancho, y otro de 6 cm de largo y 2 cm de ancho.