The length and width of a rectangle are integer.if the area is larger than its perimeter by 9 find the perimeter???
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.
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
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.
To find the perimeter of the rectangle, we need to first determine the lengths of its sides.
Let's assume the length of the rectangle is 'L' units and the width is 'W' units.
The area of a rectangle is given by the formula: Area = Length × Width.
Therefore, we have the equation: Area = L × W.
We are given that the area is larger than its perimeter by 9, so we can write another equation: Area - Perimeter = 9.
The perimeter of a rectangle is given by the formula: Perimeter = 2 × (Length + Width).
Substituting these values and equations, we have:
L × W - 2 × (L + W) = 9.
Now, let's solve this equation step by step to find the perimeter.
1. Expand the equation:
L × W - 2L - 2W = 9.
2. Rearrange the terms to group them:
L × W - 2L - 2W - 9 = 0.
3. Factor the equation by grouping:
(L - 2)(W - 2) - 13 = 0.
4. Rearrange the equation again:
(L - 2)(W - 2) = 13.
Now, we need to find the different possible pairs of (L, W) that satisfy this equation.
The pairs that satisfy (L - 2)(W - 2) = 13 are (3, 15) and (5, 7).
For the pair (3, 15):
Length - 2 = 3 - 2 = 1.
Width - 2 = 15 - 2 = 13.
For the pair (5, 7):
Length - 2 = 5 - 2 = 3.
Width - 2 = 7 - 2 = 5.
Since the length and width of a rectangle cannot be negative, we can discard the pair (3, 15).
Therefore, the only possible pair is (5, 7).
To find the perimeter, we will use the formula:
Perimeter = 2 × (Length + Width).
Substituting the values, we get:
Perimeter = 2 × (5 + 7) = 2 × 12 = 24.
Hence, the perimeter of the rectangle is 24 units.