Question

The length and width of a rectangle are integer.if the area is larger than its perimeter by 9 find the perimeter???

Answer 1

You need a new teacher. Area is different than length. Once cannot say an acre is larger than a mile, nor area is greater than perimeter by 9. It makes no sense.

Answer 2

perimeter = 2x + 2y, if x and y are length and width
area = xy

xy - 2x - 2y = 9
xy - 2y = 9 + 2x
y(x-2) = 9+2x
y = (9+2x)/(x-2) , clearly x>2

if x = 3, y = 15
area = 45, perimeter = 36 , bigger by 9, ✔

performing a long algebraic division, we can see that
(9x+2)/(x-2) = 2 + 13/(x-2)
since 13/(x-2) must be a whole number, and 13 is prime, the only value of x giving us those whole numbers is x = 3

Answer 3

I agree with Bob
I interpreted it as the numerical value of the area minus the numerical value of the perimeter is 9

The question is definitely poorly worded.