SOLUTION: A rectangle is 2 inches longer than it is wide. Numerically, its area exceeds its perimeter by 31. Find the perimeter.

Question 1170327: A rectangle is 2 inches longer than it is wide. Numerically, its area exceeds its perimeter by 31. Find the perimeter.

Found 3 solutions by josgarithmetic, ikleyn, Clanther:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
dimensions n+2 and n

perimeter

area

Condition:
.
.
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

Let x be the width, in inches; then the length is (x+2) inches. The area is x*(x+2) square inches. The perimeter is 2x + 2*(x+2) = 4x + 4 inches. The equation is x*(x+2) - (4x+4) = 31, or x^2 +2x - 4x + 2 - 4 = 31 x^2 - 2x - 35 = 0 (x-7)*(x+5) = 0. Of the two roots x= 7, x= -5, only value of 7 is positive and is the solution to the problem. The dimensions of the rectangle are 7 and 9 inches. ANSWER CHECK. The area is 7*9 = 63 sq.inches. The perimeter is 2*(7+9) = 32 inches. The difference is 63 - 32 = 31. ! Correct !

Solved.

Answer by Clanther(6)   (Show Source): You can put this solution on YOUR website!
let x be the width
let x+2 be the length
A=area
P=perimeter
A=lw
=x(x+2)
A=x²+2x
P=2x+2(x+2)
=2x+2x+4
P=4x+4
The equation is:
area-perimeter=31
(x²+2x)-(4x+4)=31
x²+2x-4x-4=31
x²-2x-4-31=0
x²-2x-35=0
by completing the square:
x²-2x+1=35+1
(x-1)²=36
√(x-1)²=±√36
x-1=±6
Take the positive value of the roots/factors
x=1+6
x=7 - the width
Substitute the value of x to the length representation:
x+2= 7+2= 9-the length
Perimeter: Substitute the positive value of the root(width) to:
P=4x+4
=4(7)+4
P=32"

RELATED QUESTIONS
A rectangle is 2 inches longer than it is wide. Numerically, its area exceeds its... (answered by mananth)
A rectangle is 3 inches longer than it is wide. Numerically, its area exceeds its... (answered by josgarithmetic,MathLover1)
A rectangle is 3 feet longer than it is wide. Its area is numerically equal to its... (answered by Fombitz)
A rectangle is 15 inches longer than its wide. Its perimeter is 150 inches. What is the... (answered by JulietG)
A rectangle is four times as long as it is wide and it's perimeter is 63 inches longer... (answered by Alan3354,josgarithmetic)
perimeter of a square is numerically greater than its area by 4. find its diagonal. (answered by htmentor)
The length of a rectangle is 2 inches longer than, its width. If the perimeter of the... (answered by solver91311)
the perimeter of a rectangle is 60 meters if its length exceeds its breath by 2 meter... (answered by sachi)
Suppose that the width of a certain rectangle is 2 inches less than its length. The area... (answered by emargo19)