Answer:
So, the width of the rectangle is 5 cm, and the length is 24 cm.
Explanation:
Let's denote the width of the rectangle as "w" and the length of the rectangle as "l." We are given two pieces of information:
1. The perimeter of the rectangle is 58 cm. Perimeter = 2(l + w).
2. The area of the rectangle is 120 cm². Area = l * w.
We are also given that the length is 4 more than four times its width, so we can write this as:
l = 4w + 4.
Now, we can create a system of equations:
Equation 1: Perimeter = 2(l + w) = 58 cm
Equation 2: Area = l * w = 120 cm²
Equation 3: Length = 4w + 4
Let's substitute Equation 3 into Equation 1 to solve for "w":
2(4w + 4 + w) = 58
2(5w + 4) = 58
10w + 8 = 58
Now, subtract 8 from both sides:
10w = 58 - 8
10w = 50
Divide by 10:
w = 5
Now that we've found the width, we can use it to find the length using Equation 3:
l = 4w + 4
l = 4(5) + 4
l = 20 + 4
l = 24
So, the width of the rectangle is 5 cm, and the length is 24 cm.
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