The length of a rectangle is three times its width. If the area of the rectangle is 300cm, find its perimeter.
Let width, W=3L (length)
Area, A = W*L = 300
Substitute W=3L
(3L)*L = 300
L²=300/3=100
L=?
post
To find the perimeter of a rectangle, we need to know the lengths of its sides. Let's first find the width of the rectangle.
Let's assume the width of the rectangle is "w" cm.
According to the problem, the length of the rectangle is three times its width. So, the length of the rectangle would be 3w cm.
Now, let's calculate the area of the rectangle:
Area of a rectangle = length × width
300 = (3w) × w
300 = 3w^2
Now, let's solve this quadratic equation to find the value of w:
3w^2 = 300
w^2 = 300 / 3
w^2 = 100
w = √100
w = 10
Now, since we have found the width of the rectangle, we can find its length:
Length = 3w = 3 × 10 = 30 cm
The width of the rectangle is 10 cm, and the length is 30 cm.
To find the perimeter of the rectangle, we can use the formula:
Perimeter = 2 × (length + width)
Substituting in the values, we get:
Perimeter = 2 × (30 + 10) = 2 × 40 = 80 cm
Therefore, the perimeter of the rectangle is 80 cm.