Question

10. The perimeter of the square and the equilateral triangle are equal. Which of the following is NOT a true statement about the figures? 10 a. The value of x is 4.5. b. The perimeter of each figure is 36 units. 2x 3x – 1.5 c. Each side length of the square measures 6 units. d. Each side length of the triangle measures 12 units.

Answer 1

We have the perimeter of the square and the triangle is equal, then:

`4\cdot(2x)=3\cdot(3x-1.5)`
`8x=9x-4.5\Rightarrow9x-8x=4.5\Rightarrow x=4.5`

The perimeter of the square is:

`8x=8\cdot4.5=36`

The perimeter of the triangle is:

`9\cdot(4.5)-4.5=36`

Each side of the triangle is:

`3\cdot(4.5)-1.5=12`

Each side of the square is:

`2\cdot4.5=9`

The only statement that is not true is, therefore, option C. Each side length of the square is 9 units (not 6 units).