twice the length L of a rectangle is equal to 3 times its width W. Its perimeter is 120 cm.
translate the English into math..
"twice the length L of a rectangle is equal to 3 times its width W"
2L = 3W
"Its perimeter is 120 cm."
2L + 2W = 120 but 2L=3W so
3W + 2W = 120
etc.
To translate the given problem into mathematical equations, we can start by representing the length of the rectangle as L and the width as W.
According to the problem, "twice the length L of a rectangle is equal to 3 times its width W," we can write this as:
2L = 3W
Next, for the statement, "Its perimeter is 120 cm," we know that the perimeter of a rectangle is the sum of all its sides. In this case, a rectangle has two equal sides (length and width) and their corresponding opposite sides are also equal.
The formula for the perimeter of a rectangle is:
Perimeter = 2(Length + Width)
Substituting L and W into the equation, we get:
2L + 2W = 120
Since we already derived the equation 2L = 3W, we can substitute 3W for 2L in the perimeter equation:
3W + 2W = 120
Simplifying this equation further will allow us to solve for the value of W, which will help us find the value of L.