Let's assume the width of the rectangle is x cm.
According to the problem, the length of the rectangle is 9.7 cm more than 4 times the width, so the length is (4x + 9.7) cm.
The formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
For this problem, we have:
91.4 = 2((4x + 9.7) + x) cm
Simplifying the equation:
91.4 = 2(5x + 9.7) cm
91.4 = 10x + 19.4 cm
91.4 - 19.4 = 10x cm
72 = 10x cm
x = 7.2 cm
Now, we have the width of the rectangle, which is 7.2 cm.
Substituting the value of x back into the equation for the length, we get:
Length = 4x + 9.7 cm
Length = 4(7.2) + 9.7 cm
Length = 28.8 + 9.7 cm
Length = 38.5 cm
Therefore, the dimensions of the rectangle are:
Width = 7.2 cm
Length = 38.5 cm
Note: Enter your answer and show all the steps that you use to solve this problem.
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?
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