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The length of a rectangle is 9.7 cm more than 4 times the width. If the perimeter of the rectangle is 91.4 cm, what are its dimensions?
Let's assume the width of the rectangle is "w" cm.
According to the given information, the length of the rectangle is 9.7 cm more than 4 times the width. So, the length can be expressed as 4w + 9.7 cm.
The perimeter of the rectangle is given as 91.4 cm, which can be expressed as the sum of all four sides of the rectangle.
Perimeter = 2(length + width)
Substituting the values, we have:
91.4 = 2((4w + 9.7) + w)
Let's simplify the equation:
91.4 = 2(5w + 9.7)
91.4 = 10w + 19.4
Now, we can solve for "w":
10w = 91.4 - 19.4
10w = 72
w = 72/10
w = 7.2 cm
Now, we can substitute the value of "w" back into the equation to find the length:
Length = 4w + 9.7
Length = 4(7.2) + 9.7
Length = 28.8 + 9.7
Length = 38.5 cm
So, the dimensions of the rectangle are:
Width = 7.2 cm
Length = 38.5 cm