The ration of the length of a rectangle to its breadth is 9:4. If the perimeter of the rectangle is 104 cm. find the area of the rectangle.
Width = W cm.
Length = 9.4W cm.
2W + 2*9.4W = 104 cm.
2W + 18.8W = 104
20.8W = 104
W = 5 cm.
L = 9.4W = 9.4*5 = 47 cm.
A = L*W = 47 * 5 = 235 cm^2.
To find the area of the rectangle, we first need to find the length and breadth of the rectangle.
Given that the ratio of the length to the breadth is 9:4, let's assume the length is 9x and the breadth is 4x.
The perimeter of a rectangle is calculated by adding all the sides together, so we can write the equation:
Perimeter = 2(length + breadth)
Substituting in the given values, we have:
104 = 2(9x + 4x)
Simplifying the equation:
104 = 2(13x)
104 = 26x
Divide both sides by 26:
x = 4
Now we know that x is equal to 4, we can find the length and breadth of the rectangle:
Length = 9x = 9 * 4 = 36 cm
Breadth = 4x = 4 * 4 = 16 cm
To find the area of the rectangle, we use the formula:
Area = Length * Breadth
Substituting in the values we found:
Area = 36 cm * 16 cm
Area = 576 cm^2
Therefore, the area of the rectangle is 576 square centimeters.