Question

The perimeters of the square and equilateral triangle shown below are equal. Which of the following is NOT a true statement about the figures. Remember: perimeter of a square = 4(one side), and perimeter of an equilateral triangle = 3(one side)

Answer 1

The incorrect option is Each side length of the square is 6 units

Step-by-step explanation

We are given that the perimeter of the square and the equilateral triangle are equal.

The length of the side of the square is 2x.

The perimeter of a square is given as:

P = 4 * L

=> P = 4 * 2x

P(square) = 8x

The length of side of the triangle is given as 3x - 1.5.

The perimeter of an equilateral triangle is given as:

P = 3 * L

=> P = 3 * (3x - 1.5)

P(triangle) = 9x - 4.5

Therefore, since both perimeters are equal:

8x = 9x - 4.5

Collect like terms:

9x - 8x = 4.5

x = 4.5

Now, for the options:

- The value of x is 4.5

- The perimeter of the square is 8 * 4.5 i.e. 36 units.

- Each side length of the square is 2 * 4.5 = 9 units

- Each side length of the triangle is :

3 * 4.5 - 1.5 = 13.5 - 1.5 = 12 units

So, the incorrect option is Each side length of the square is 6 units