the length of a rectangular piece of land is 40 cm more than two times its width. the perimeter is 680 cm. Find its dimensions
P = 2L + 2W
680 = 2(2W + 40) + 2W
680 = 4W + 80 + 2W
600 = 6W
100 = W
Let's assume the width of the rectangular piece of land is "w" cm.
According to the given information, the length of the land is "40 cm more than two times its width". So, the length can be expressed as: 2w + 40 cm.
The perimeter of a rectangle is given by the formula: 2(length + width). Since the perimeter is given as 680 cm, we can set up the equation:
2(2w + 40 + w) = 680
Simplifying the equation:
2(3w + 40) = 680
6w + 80 = 680
6w = 600
w = 100
So, the width of the rectangular piece of land is 100 cm.
Now, we can find the length using the formula: length = 2w + 40.
length = 2(100) + 40
length = 240
Therefore, the dimensions of the rectangular piece of land are:
Width: 100 cm
Length: 240 cm
To find the dimensions of the rectangular piece of land, we can set up an equation using the given information.
Let's assume the width of the land is "w" cm.
According to the given information, the length of the land is 40 cm more than two times its width. So, the length can be expressed as 2w + 40 cm.
The perimeter of a rectangle is calculated by adding the lengths of all its sides. For a rectangle, the perimeter is equal to two times the length plus two times the width. So, we can set up the equation:
2(length) + 2(width) = perimeter
Substituting the values we know:
2(2w + 40) + 2w = 680
Now we can solve this equation to find the value of "w", which represents the width of the piece of land:
4w + 80 + 2w = 680
6w + 80 = 680
6w = 600
w = 100
Therefore, the width of the piece of land is 100 cm.
To find the length, we can substitute the value of the width back into the expression for the length:
Length = 2w + 40
Length = 2(100) + 40
Length = 200 + 40
Length = 240
Therefore, the length of the piece of land is 240 cm.
Hence, the dimensions of the rectangular piece of land are 100 cm (width) and 240 cm (length).