The area of a rectangle whose length is 5 more than twice its width is 75 square unit. What is the perimeter of the rectangle?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 40 units
The area of a rectangle is length \(\times\) width and its perimeter is \(2(\text{length}+\text{width})\). Writing the length in terms of the width gives a quadratic equation for the width.
The length and the width (the length is 5 more than twice the width):
Width \(=w\)
Length \(=2w+5\)
Finding \(w\) (length × width is the area 75):
\(w(2w+5)=75\)
So \(2w^2+5w-75=0\)
\((2w+15)(w-5)=0\)
A width cannot be negative, so \(w=5\)
The perimeter (putting \(w=5\) in the length):
Length \(=2\times5+5=15\)
Perimeter \(=2(15+5)=40\) units