the length of a rectangle is 5cm longer than its width and its area is 66cm square. find the perimeter of the rectangle
66 = 6*11
To find the perimeter of the rectangle, we need to know both the length and width of the rectangle.
Let's assume the width of the rectangle is "x" cm.
According to the given information, the length of the rectangle is 5 cm longer than its width. So, the length would be "x + 5" cm.
The formula to calculate the area of a rectangle is: Area = Length x Width.
Given that the area is 66 cm square, we can set up the following equation:
66 = (x + 5) * x
To solve this equation and find the width (x), we can rewrite the equation in quadratic form:
x^2 + 5x - 66 = 0
Now, we can factorize the quadratic equation:
(x + 11)(x - 6) = 0
From this equation, we get two possible solutions for the width:
x + 11 = 0 => x = -11 (rejected as width cannot be negative)
x - 6 = 0 => x = 6
Therefore, the width of the rectangle is 6 cm.
Now, we can find the length of the rectangle:
Length = Width + 5 = 6 + 5 = 11 cm
The perimeter of a rectangle can be calculated using the following formula:
Perimeter = 2 * (Length + Width)
Substituting the values, we get:
Perimeter = 2 * (11 + 6) = 2 * 17 = 34 cm
So, the perimeter of the rectangle is 34 cm.
To find the perimeter of a rectangle, we first need to calculate the dimensions of the rectangle. In this case, we know that the length of the rectangle is 5cm longer than its width.
Let's assume the width of the rectangle as "W" (in cm). Therefore, the length of the rectangle would be "W + 5" (in cm).
The formula for the area of a rectangle is length multiplied by width. In this case, the area is given as 66 cm square. So we can write the equation as follows:
(W + 5) * W = 66
Now, we can simplify this equation by expanding and rearranging it:
W^2 + 5W = 66
Rearranging the equation gives us:
W^2 + 5W - 66 = 0
Now, we can solve this quadratic equation by factoring or by using the quadratic formula.
Factoring:
(W + 11)(W - 6) = 0
Setting each factor to zero gives us two possible values for the width:
W + 11 = 0 --> W = -11 (Since width cannot be negative)
W - 6 = 0 --> W = 6
Since we need a positive value for the width, we disregard W = -11 and take W = 6 as the width of the rectangle.
So, the width is 6 cm, and the length is 6 cm + 5 cm = 11 cm.
Now, we can calculate the perimeter of the rectangle:
Perimeter = 2(length + width)
Perimeter = 2(11 cm + 6 cm)
Perimeter = 2 * 17 cm
Perimeter = 34 cm
Therefore, the perimeter of the rectangle is 34 cm.