Question
1. The length of a rectangle is 5.4 cm more than 3 times the width. If the perimeter of the rectangle is 80.4 cm, what are its dimensions? Please show your work.
Answers
GPT 3.5
Let's call the width of the rectangle "x" cm.
According to the problem, the length of the rectangle is 5.4 cm more than 3 times the width, so the length is 3x + 5.4 cm.
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width).
Substituting the values, we have:
80.4 cm = 2(3x + 5.4 cm + x)
Simplifying the equation:
80.4 cm = 2(4x + 5.4 cm)
80.4 cm = 8x + 10.8 cm
80.4 cm - 10.8 cm = 8x
69.6 cm = 8x
x = 69.6 cm / 8
x = 8.7 cm
So the width of the rectangle is 8.7 cm.
Now we can find the length:
Length = 3x + 5.4 cm
Length = 3(8.7 cm) + 5.4 cm
Length = 26.1 cm + 5.4 cm
Length = 31.5 cm
Therefore, the dimensions of the rectangle are width = 8.7 cm and length = 31.5 cm.
According to the problem, the length of the rectangle is 5.4 cm more than 3 times the width, so the length is 3x + 5.4 cm.
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width).
Substituting the values, we have:
80.4 cm = 2(3x + 5.4 cm + x)
Simplifying the equation:
80.4 cm = 2(4x + 5.4 cm)
80.4 cm = 8x + 10.8 cm
80.4 cm - 10.8 cm = 8x
69.6 cm = 8x
x = 69.6 cm / 8
x = 8.7 cm
So the width of the rectangle is 8.7 cm.
Now we can find the length:
Length = 3x + 5.4 cm
Length = 3(8.7 cm) + 5.4 cm
Length = 26.1 cm + 5.4 cm
Length = 31.5 cm
Therefore, the dimensions of the rectangle are width = 8.7 cm and length = 31.5 cm.