Question

The length of a rectangle is the sum of the width and 4. The area of the rectangle is 32

Answer 1

Answer:

The width of rectangle w = 4 units

Step-by-step explanation:

We are given:

Width of rectangle = w

Length of rectangle = w+ 4

Area of rectangle = 32 units

We need to find width of the rectangle

The formula used is: $Area\:of\:rectangle=Length\times Width$

Putting values and finding width of rectangle

$Area\:of\:rectangle=Length\times Width\\32=(w+4)\times w\\32=w^2+4w\\w^2+4w-32=0$

We need to solve this quadratic equation to find width (w)

We will use factorisation and break the middle term.

$w^2+4w-32=0\\w^2+8w-4w-32=0\\w(w+8)-4(w+8)=0\\(w-4)(w+8)=0\\w-4=0\:or\:w+8=0\\w=4\:or\:w=-8$

Since width of rectangle can't be negative, so rejecting w=-8

Therefore, the width of rectangle w = 4 units