One side of a rectangle is longer than the other side by 1cm. If the area is 30cm, find its perimeter.
shorter side --- x
longer side ---- x + 1
x(x+1) = 30
x^2 + x - 30 = 0
(x+6)(x-5) = 0
x = -6 or x = 5, but a side can't be negative, so
x = 5
short side is 5
long side is 6
perimeter = 2(5) + 2(6) = 22
To find the perimeter, we need to know the lengths of both sides of the rectangle. Let's call one side x cm and the other side (x+1) cm, as given in the problem.
We are also given that the area of the rectangle is 30 cm². The formula for the area of a rectangle is A = length × width. In this case, A = 30 cm².
So we have the equation x(x+1) = 30.
To solve this equation and find the values of x, we can expand it by multiplying:
x² + x = 30.
Rearranging the equation, we get:
x² + x - 30 = 0.
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's solve it by factoring:
(x + 6)(x - 5) = 0.
From this equation, we find two possible values for x: x = -6 or x = 5. However, since we are dealing with the length of a side, the distance cannot be negative. Therefore, we discard the negative value and take x = 5 cm.
Now that we have the length of one side, we can find the other side by adding 1 cm. So, the length of the longer side is (x+1) = 6 cm.
To find the perimeter, we add up all the sides of the rectangle:
Perimeter = 2(length + width)
Perimeter = 2(5 cm + 6 cm)
Perimeter = 2(11 cm)
Perimeter = 22 cm.
Therefore, the perimeter of the rectangle is 22 cm.