the length of a rectangular garden is 5 meters more than 3 times its width. The perimeter of the garden is 74 meters. What are the dimensions of the garden?
P=2l+2w
l=3w+5
P=2(3w+5)+2w solve for w, then solve for l
W=5/8
L=15/8+5
5x3=15
74+15=89
To determine the dimensions of the rectangular garden, we can set up a system of equations based on the given information:
Let's denote the width of the garden as x (in meters).
According to the problem, the length of the garden is 5 meters more than 3 times its width, which can be expressed as 3x + 5.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 74 meters.
So, we can set up the equation:
2(length + width) = perimeter
Substituting the values we have, we get:
2(3x + 5 + x) = 74
Simplifying the equation:
2(4x + 5) = 74
8x + 10 = 74
8x = 64
x = 64 / 8
x = 8
Therefore, the width of the garden is 8 meters.
To find the length, we can substitute the value of x into the expression for length:
Length = 3x + 5
Length = 3(8) + 5
Length = 24 + 5
Length = 29
Therefore, the dimensions of the garden are 29 meters (length) and 8 meters (width).