Let the width of the rectangle = x units

Length = (2 x + 5) units

According to the question,

Area = x(2x + 5)

=> 75 = \( \Large 2x^{2}+5x \)

=> \( \Large 2x^{2} +5x-75=0\)

=> \( \Large 2x^{2} +15x-10x-75=0\)

=> x(2x+15)-5(2x+15)=0

=> (2x+15)(x-5)=0

=> x = 5 and \( \Large \frac{-15}{2} \)

Width cannot be negative.

Width = 5 units

Length=2x+5 =\( \Large 2\times 5+5 \)=15 units

Perimeter of the rectangle

= 2(15 + 5) = 40 units