Question

Two opposite sides of a rectangle are each of length x. If the perimeter of the rectangle is 12, then the area, as a function of x, is
x(12 – x)
x(6 – x)
(6 – x) 2
x(12 – 2x)

Answer 1

Answer: $x(6-x)$

Step-by-step explanation:

Given : Two opposite sides of a rectangle are each of length x.

Let the other adjacent side be y.

The perimeter of the rectangle is 12 units.

Perimeter of rectangle is given by :-

$P=2(\text{Sum of adjacent sides})\\\\\Rightarrow\ 12=2(x+y)\\\\\Rightarrow\ x+y=\dfrac{12}{2}=6\\\\\Rightarriow\ y=6-x$

The area of rectangle is given by :-

$A=\text{product of two adjacent sides}\\\\\Rightarrow\ A=xy=x(6-x)$

Hence, the area as a function x = $x(6-x)$

Answer 2

Answer:

option B

Step-by-step explanation:

given,

two opposite side of rectangle of each length = x

perimeter of the rectangle = 12

let the unknown sides be y

perimeter of the rectangle

          2 x + 2 y = 12

                    y = 6 -x

hence, we know area of the triangle will be  (length × breadth)

                   = x × y

                   = x × ( 6 - x )

so, area of rectangle will be x(6-x) correct answer will be option B