Question

The perimeter (distance around the shape) of a rectangle is 40 cm. The length is 14 cm. Let x = width of the rectangle.

Ravi says he can find the width using the equation 2(x + 14) = 40
Fran says she can find the width using the equation 2x + 28 = 40.
Answer the questions to solve the equations and to compare the steps and solutions.
The two equations have different solution steps. Do they have the same solution? Why or why not?"

Answer 1

No, the two equations do not have the same solution. The width of the rectangle is 6 cm.

Step-by-step explanation:

No, the two equations do not have the same solution. Let's solve each equation step by step:

Ravi's equation: 2(x + 14) = 40

Distribute 2 through the parentheses: 2x + 28 = 40

Subtract 28 from both sides: 2x = 12

Divide both sides by 2: x = 6

Fran's equation: 2x + 28 = 40

Subtract 28 from both sides: 2x = 12

Divide both sides by 2: x = 6

As you can see, both equations lead to the same solution. The width of the rectangle is 6 cm.