Use an algebraic equation to solve the problem.
A rectangle is 3 times as long as it is wide. The perimeter is 60 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary.
Responses:
a) 7.5 cm by 22.5 cm
b) 7.5 cm by 52.5 cm
c) 20 cm by 60 cm
d) 15 cm by 22.5 cm
Let the width of the rectangle be x cm. Therefore, the length of the rectangle is 3x cm.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Substituting the values into the formula:
60 = 2(3x + x)
Simplifying the equation:
60 = 2(4x)
30 = 4x
x = 7.5
Therefore, the width of the rectangle is 7.5 cm, and the length is 3 times that, which is 22.5 cm.
The correct answer is a) 7.5 cm by 22.5 cm
Let's assume that the width of the rectangle is 'w'. According to the problem, the length of the rectangle is 3 times the width, so the length can be represented as '3w'.
The perimeter of a rectangle is given by the formula P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
Given that the perimeter is 60 cm, we can set up the equation:
60 = 2(3w + w)
Simplifying the equation, we have:
60 = 2(4w)
Dividing both sides by 2, we get:
30 = 4w
Dividing both sides by 4, we have:
7.5 = w
Therefore, the width of the rectangle is 7.5 cm.
The length of the rectangle is 3 times the width, so the length is:
3(7.5) = 22.5 cm
Therefore, the dimensions of the rectangle are 7.5 cm by 22.5 cm.
So the correct answer is option a) 7.5 cm by 22.5 cm.