Please help me with this?

Question

A rectangle has a length twice its width. A square with the same area has a side 2 units longer than the width of the rectangle. Find the dimensions of the rectangle.

Answer 1

Draw it out and let x equal the amount that you don't know.

So, x= width of rectanglee

2x=length of rectangle

x+2 = side of the square

You know that the area of the rectangle and the square are equal

x * 2x = (x+2) * (x+2)

2x^2= x^2 +4x+4

x^2 - 4x-4=0  

You need to factorise this now, if you have any questions with how I have factorised it just email me and ask!

(x-2)^2 -4-4=0

(x-2)^2=8

(x-2) = root8

x= 2 plus/minus root8

So since it can't be a negative number your answer for x = 2+ root8

So your dimensions would be width= 2+ root8, length  2(2+ root8)