Question

the perimeter of a rectangle is 50 inches. the length of the rectangle is 10 inches. which method can be used to find w, the width of the rectangle? solve for w in the equation 2w + 10 = 50. divide 50 by 2 and then add 10. divide 50 by the product of 10 and 2. solve for w in the equation 2(w + 10) = 50.

Explanation:

To determine the correct method, we start by recalling the formula for the perimeter of a rectangle: \( P = 2(l + w) \), where \( P \) is the perimeter, \( l \) is the length, and \( w \) is the width. We know \( P = 50 \) inches and \( l = 10 \) inches.

Step 1: Substitute the known values into the perimeter formula

Substitute \( P = 50 \) and \( l = 10 \) into \( P = 2(l + w) \):
\( 50 = 2(10 + w) \)

Now, let's analyze each option:

1. "Divide 50 by 2 and then add 10":

Dividing 50 by 2 gives \( \frac{50}{2} = 25 \). Adding 10 would give \( 25 + 10 = 35 \), which is not the width. This is incorrect.

1. "Solve for \( w \) in the equation \( 2w + 10 = 50 \)":

The perimeter formula is \( P = 2(l + w) \), not \( P = 2w + l \). Substituting \( l = 10 \) and \( P = 50 \) does not give \( 2w + 10 = 50 \). This is incorrect.

1. "Divide 50 by the product of 10 and 2":

The product of 10 and 2 is \( 10 \times 2 = 20 \). Dividing 50 by 20 gives \( \frac{50}{20} = 2.5 \), which is not the width. This is incorrect.

1. "Solve for \( w \) in the equation \( 2(w + 10) = 50 \)":

This matches the perimeter formula \( P = 2(l + w) \) with \( l = 10 \) and \( P = 50 \). Solving this equation will give the correct width.

To confirm, solve \( 2(w + 10) = 50 \):

• Divide both sides by 2: \( w + 10 = \frac{50}{2} = 25 \)
• Subtract 10 from both sides: \( w = 25 - 10 = 15 \)

Thus, the correct method is to solve for \( w \) in the equation \( 2(w + 10) = 50 \).

Answer:

Solve for \( w \) in the equation \( 2(w + 10) = 50 \)