Answer:
Step-by-step explanation:
The relation between length and width can be used with the formula for the perimeter of a rectangle to find the dimensions.
Let the rectangle width in yards be represented by w. Then the length is (2w+1). The perimeter formula is ...
P = 2(L +W) . . . . . . where L and W are the length and width
Filling in the given values, we have ...
218 = 2((2w+1) +w)
Dividing by 2 and simplifying the results, we have ...
109 = 3w +1
108 = 3w . . . . . . . subtract 1
36 = w . . . . . . . . . divide by 3
2w+1 = 2(36) +1 = 73 . . . . find the length
The length of the rectangle is 73 yards; the width is 36 yards.
The length and the width of the given rectangle are 73 yards and 36 yards.
It is given that the length of a rectangle is 1 yard more than twice the width.
The perimeter of the rectangle is 218 yards.
We are to find the length and width of the given rectangle.
A rectangle is a quadrilateral with four right angles.
The area of a rectangle is given by:
Length x width
The perimeter of a rectangle is given by:
= Length + Length + width + width
= 2 ( length + width ).
The length of a rectangle is 1 yard more than twice the width.
we can write this as:
Length = 1 yard + 2 width -------------------(1)
The perimeter is 218 yards.
We can write it as:
2 ( length + width ) = 218 yards ---------------(2)
Substituting (1) in (2).
we get,
2 ( 1 yard + 2 width + width ) = 218 yards
2 ( 1 yard + 3 width ) = 218 yards
2 x 1 yards + 2 x 3 width = 218 yards
2 yards + 6 width = 218 yards
6 width = 218 yards - 2 yards
6 width = 216 yards
Width = 216 / 6 yards
Width = 36 yards ------------------------(3)
Putting (3) in (1) we get,
Length = 1 yard + 2 width
Length = 1 yard + 2 x 36 yards
Length = 1 yard + 72 yards
Length = 73 yards
Thus, the length and the width of the given rectangle are 73 yards and 36 yards.
Learn more about rectangles here:
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