Question

A student is given the rectangle and the square shown. The student states that the two figures have thesame perimeter. Is the student correct? Complete the explanation to explain your reasoning.X + 10X +5хX +5The student is (select) The perimeter of a figure is found by (select)For the rectangle, the perimeter isFor the square, the perimeterthe lengths of its sides,is

Answer 1

Given:

The length of sides of rectangle is x + 10 and x.

The length of side of square is x + 5.

Explanation:

The perimeter of any figure is obtained by adding all the sides of the given figure.

Determine the perimeter of rectangle.

$\begin{gathered} P\text{ (Rectangle)}=x+10+x+x+10+x \\ =4x+20 \end{gathered}$

Determine the perimeter of square.

$\begin{gathered} P\text{ (Square)}=x+5+x+5+x+5+x+5 \\ =4x+20 \end{gathered}$

So perimeter of both figures (rectangle and square) is equal.

So answer is,

The student is Correct. The perimeter of a figure is found by adding the lengths of its sides. For the rectangle, the perimeter is 4x + 20. For the square, the perimeter is 4x + 20.