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

option B

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

Answer 2

Answer:
`x(6-x)`

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=(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)`