The length of a rectangle is a two-digit number with identical digits (aa) The width is 1/10 of the length. The perimeter is 2 times the area of the rectangle.

Question

For my MATH106 College Course

Answer 1

Let x = units digit of the length

 

Then 10x = tens digit of the length

 

So, the length is 10x+x = 11x

 

Width = (11/10)x

 

Perimeter = 2(11x) + 2(11/10)x

 

Area = (11x)(11/10)x

 

Perimeter = 2(Area), so 2(11x) + 2(11/10)x = 2(11x)(11/10)x

 

Divide by 2:  11x + (11/10)x = (11x)(11/10)x

 

Multiply by 10:  110x + 11x = 121x²

 

                                 121x = 121x²

 

                                      x² - x = 0

 

                                      x(x-1) = 0   x = 0 or 1

 

Since x can't be 0, x = 1

 

Length = 11, Width = 11/10