Question

A student is given the rectangle and the square shown. The student states that the two figures have the same perimeter. Is the student correct? Complete the explanation to explain your reasoning.

rectangle= (x+15)*x
square= (x+9)*(x+=9)

The student is ____. The perimeter of a figure is found by_____the lengths of its sides. For the rectangle, the perimeter is____. For the square, the perimeter
is____.

Answer 1

The student is incorrect. The perimeter of a figure is found by adding the lengths of its sides. For the rectangle, the perimeter is 4x + 30. For the square, the perimeter is 4x + 36

Explanation:

Given

`Rectangle = (x + 15) * x`

`Square = (x + 9) * (x + 9)`

Required

Fill in the gaps

The area of a rectangle is

`Area = Length * Width`

Comparing this formula to
`Rectangle = (x + 15) * x`

We have that:

`Length = x + 15`

`Width = x`

Perimeter of the rectangle is calculated as:

`Perimeter = 2 * (Length + Width)`

`Perimeter = 2 * (x + 15 + x)`

`Perimeter = 2 * (2x + 15)`

`Perimeter = 4x + 30`

Similarly, for the square:

`Area = Length * Length`

Compare this to
`Square = (x + 9) * (x + 9)`

We have that:

`Length = x + 9`

The perimeter is calculated as:

`Perimeter = 4 * Length`

`Perimeter = 4 * (x + 9)`

`Perimeter = 4x + 36`

Since the perimeters of both shapes are not equal, then the student is incorrect