A rectangle has a perimeter of 360 m. If its length and width are in the ratio of 5:4 respectively, what would be its area?
A: 800 m²
B: 8000 m²
C: 100 m²
D: 1000 m²
The perimeter of a rectangle is given by the formula :
p = 2×(Length + Width).
Let's denote the length of the rectangle as 5x and the width as 4x, where x is a common multiplier.
Given that the perimeter is 360 m, we can set up the equation:
2 × ( 5x + 4x ) = 360
Combine like terms:
2 × 9x = 360
Simplify:
18x = 360
Now, solve for x:
X = 360/18 = 20
Now that we have the value of x, we can find the length and width of the rectangle:
Length = 5x = 5 × 20 = 100m
Width = 4x = 4 × 20 = 80m
Now, calculate the area of the rectangle using the formula Area=length×width:
Area = 100m × 80m
Area = 8000m²
So, the area of the rectangle is 8000m²
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