The perimeter(P 2l+2w)of a rectangle is 18 cm. If w is the width of the rectangle and L is the length, which graph below shows the relationship between the width and the length of the rectangle?
Answers
the question does not present the options, but thisdoes not interfere with the resolution
we know that
Perimeter of rectangle=2*[W+L]
where
L is the length of rectangle
W is the width of rectangle
Perimeter=18 cm
so
18=2*[W+L]-----> divide by 2------> 9=W+L
Let
x-------> L
y-------> W
then
x+y=9
using a graph tool
see the attached figure
the slope of the line is m=1
the x intercept is the point (9,0)
the y intercept is the point (0,9)
Final answer:
The relationship between the width and length of a rectangle given a constant perimeter is inverse; as the length increases, the width decreases proportionally. The graph representing this relationship would feature the length on the x-axis and width on the y-axis, and the line would represent all pairs of length and width that satisfy the equation
Explanation:
The problem in question asks to find the relationship between the width and length of a rectangle given its perimeter. In the given expression,
P = 2l + 2w
, where P is the perimeter, l is the length, and w is the width of the rectangle. Given that P = 18 cm, the relationship between the width and length can be represented by the equation
w = (P - 2l)/2
which implies that as the length increases the width decreases proportionally to maintain the constant perimeter. We must then create a graph where the x-axis represents the length and the y-axis represents the width, and a line representing possible solutions (l, w) that satisfy both the equation and the conditions given (length and width must be greater than 0).
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