Question

the perimeters of the square and the equilateral triangle shown are equal. mark each statement below as true or false. if false, rewrite the statement correctly.
__ 8. the situation can be represented by 2.5x - 3 = 2x - 2.
__ 9. the value of x = 3.
__ 10. the perimeter of each shape is 3 units.
©maneuvering the middle llc, 2016

Explanation:

Step1: Find the correct equation

The perimeter of a square is \(4\times\) side length. The side length of the square is \(2.5x - 3\), so its perimeter is \(4(2.5x - 3)=10x-12\).
The perimeter of an equilateral triangle is \(3\times\) side length. The side length of the triangle is \(2x - 2\), so its perimeter is \(3(2x - 2)=6x - 6\).
Since perimeters are equal, the equation is \(10x-12 = 6x - 6\). So statement 8 is false.

Step2: Solve for \(x\)

For the equation \(10x-12 = 6x - 6\)
Subtract \(6x\) from both sides: \(10x-6x-12=6x - 6-6x\)
\(4x-12=-6\)
Add \(12\) to both sides: \(4x-12 + 12=-6+12\)
\(4x=6\)
Divide both sides by \(4\): \(x=\frac{6}{4}=1.5\)
So statement 9 is false.

Step3: Find the perimeter

Substitute \(x = 1.5\) into the perimeter formula of the square (or triangle).
Using the square's perimeter formula \(P=10x-12\), \(P=10\times1.5-12=15 - 12=3\)
Using the triangle's perimeter formula \(P=6x - 6\), \(P=6\times1.5-6=9 - 6=3\)
So statement 10 is true.

Answer:

1. False. The correct equation is \(10x-12 = 6x - 6\).
2. False. The value of \(x = 1.5\).
3. True.