Question

If the length of the rectangle measures (2x -4) cm and the width measures (3x) cm, what is the area of the rectangle in terms of x?

Answer 1

If one side of a rectangle is (2x + 4) then the opposite side is also (2x + 4). Their sum is (4x + 8). Since the perimeter is (6x + 4) we subtract (4x + 8), which yields the sum of the other two sides: (2x - 4). Since they too are equal we divide (2x + 4) by 2: (x - 2). The area of a rectangle is length times width, so the area of this rectangle is (x - 2)(2x + 4) or 2x^2 - 8.

Answer 2

Given: The length of the rectangle measures$(2x -4)$ cm and the width measures $(3x)$cm.

We have to find the area of the rectangle in terms of x.

As we know that the formula is used to calculate the area of a rectangle is:

$A=l\times w$

Where,

l = length

w = width

We are solving in the following way:

We have,

The length of the rectangle measures$(2x -4)$ cm and the width measures $(3x)$cm.

Here,

l = $(2x -4)$ cm.

w = $(3x)$cm.

So, the area of a rectangle will be:

$A=l\times w$

$A=(2x -4)\times (3x)\\A= 6x^{2} -12$

Hence, the area of a rectangle is$(6x^{2} -12)cm^{2}$.