Question

1. the length of a rectangle is twice the width.

a. find the width if the perimeter is 60cm.
b. define a variable, write an equation, and solve the problem.

Explanation:

Part (a)

Step 1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Let the width be \( w \). Since the length is twice the width, the length \( l = 2w \).

Step 2: Substitute into the perimeter formula

We know \( P = 60 \) cm. Substitute \( l = 2w \) and \( P = 60 \) into the formula: \( 60 = 2\times(2w + w) \).

Step 3: Simplify the equation

First, simplify inside the parentheses: \( 2w + w = 3w \). So the equation becomes \( 60 = 2\times3w \), which simplifies to \( 60 = 6w \).

Step 4: Solve for \( w \)

Divide both sides of the equation by 6: \( w=\frac{60}{6}=10 \).

Step 1: Define the variable

Let \( w \) represent the width of the rectangle (in centimeters). Then the length \( l = 2w \) (since length is twice the width).

Step 2: Write the equation

Using the perimeter formula \( P = 2(l + w) \), and substituting \( l = 2w \) and \( P = 60 \), we get:
\( 60 = 2(2w + w) \)

Step 3: Solve the equation

Simplify inside the parentheses: \( 2w + w = 3w \), so the equation is \( 60 = 2\times3w \) or \( 60 = 6w \).
Divide both sides by 6: \( w=\frac{60}{6}=10 \).

Answer:

The width is \( 10 \) cm.

Part (b)