The area of a rectangle is 60 cm squared and its perimeter is 38cm. Find the length and width of a lectangle

The length of a board is twice its width. If its perimeter is 3.60m,its width will be how many in cm

To find the length and width of the rectangle, we can use the given information about the area and perimeter.

Let's assume the length of the rectangle is L and the width is W.

1. Find the equation for the area of the rectangle:
Area of a rectangle = Length × Width
Given that the area is 60 cm², we have:
L × W = 60 --------(Equation 1)

2. Find the equation for the perimeter of the rectangle:
Perimeter of a rectangle = 2 × (Length + Width)
Given that the perimeter is 38 cm, we have:
2(L + W) = 38 --------(Equation 2)

Now, we have a system of two equations (Equations 1 and 2) with two variables (L and W) that we can solve simultaneously.

To solve the system of equations, we have a few options. One method is substitution:

1. Rearrange Equation 1 to solve for L:
L = 60/W

2. Substitute the value of L from Equation 1 into Equation 2:
2((60/W) + W) = 38

Simplify the equation:
(120/W) + 2W = 38

Multiply through by W to eliminate the fraction:
120 + 2W² = 38W

3. Rearrange the equation to form a quadratic equation:
2W² - 38W + 120 = 0

Now, we can solve this quadratic equation to find the possible values of W.

You can either factorize the equation or use the quadratic formula to solve for W.

4. Once you have the value(s) of W, substitute them back into one of the original equations to find the corresponding value(s) of L.

By following these steps, you'll be able to find the length and width of the rectangle.

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