a rectangular garden has a perimeter of 140m.its width is three quarter of its length.
what is the length and width?
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if the length is x, the width is 3/4 x
2(x + 3/4 x) = 140
7/4 x = 70
x = 40
so the garden is 30 x 40
To solve this problem, we need to set up equations based on the information given.
Let's assume that the length of the rectangular garden is represented by 'L' and the width is represented by 'W'.
1. We know that the perimeter of a rectangle is given by the formula: Perimeter = 2(L + W). So, for this garden, the perimeter is 140m. We can set up an equation:
2(L + W) = 140
2. We are also given that the width (W) is three-quarters (3/4) of the length (L). We can represent this in an equation:
W = (3/4)L
Now, we have a system of two equations with two variables. We can solve them simultaneously to find the values of length and width.
Let's substitute the value of W from the second equation into the first equation:
2(L + (3/4)L) = 140
2(7/4)L = 140
(7/4)L = 70
L = (4/7) * 70
L = 40
Now that we have the value for length (L = 40), we can substitute it back into the second equation to find the width (W):
W = (3/4)L
W = (3/4) * 40
W = 30
Therefore, the length of the rectangular garden is 40m, and the width is 30m.