Let the width of the rectangle be represented as w. According to the problem, the length l can be expressed as:
l = 4w + 97
The perimeter P of a rectangle can be calculated using the formula:
P = 2(l + w)
Substituting the given perimeter value:
914 = 2(l + w)
We can simplify this equation to:
457 = l + w
Now, substituting the expression for length in terms of width into this equation:
457 = (4w + 97) + w
Combine like terms:
457 = 5w + 97
Next, isolate w by subtracting 97 from both sides:
457 – 97 = 5w
360 = 5w
Now, divide both sides by 5:
w = 72
Having determined the width, we can find the length:
l = 4(72) + 97 = 288 + 97 = 385
Thus, the dimensions of the rectangle are:
- Width: 72 cm
- Length: 385 cm