The sides of a rectangle can be represented by consecutive even numbers. It’s area is 48. Find the dimensions of the rectangle.

Question

explanation, step by step and working out please

Answer 1

Consecutive even numbers are separated by 2

Let the numbers be x, x+2

 

So the area is x(x+2)

 

x(x+2) = 48

x² + 2x = 48

x² + 2x - 48 = 0

This can be factored. The factors of -48 that add to 2 are 8(-6)

(x+8)(x-6) = 0

 

x = -8 or x = 6

 

We use x=6 since it will be a positive number

x+2 = 8

 

The rectangle is 8 by 6