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.

1. the situation can be represented by ( 2.5x - 3 = 2x - 2 ).
2. the value of ( x = 3 ).
3. the perimeter of each shape is 3 units.

Explanation:

Step1: Find the correct equation

The perimeter of a square with side length \(s\) is \(P = 4s\), and the perimeter of an equilateral triangle with side length \(t\) is \(P=3t\).
If the side - length of the square is \(2.5x - 3\) and the side - length of the equilateral triangle is \(2x - 2\), then the equation for equal perimeters is \(4(2.5x - 3)=3(2x - 2)\).
Expand the left - hand side: \(4\times2.5x-4\times3 = 10x-12\).
Expand the right - hand side: \(3\times2x-3\times2=6x - 6\).
So the equation is \(10x-12 = 6x - 6\).

Step2: Solve the equation \(10x-12 = 6x - 6\)

Subtract \(6x\) from both sides: \(10x-6x-12=6x - 6-6x\), which gives \(4x-12=-6\).
Add \(12\) to both sides: \(4x-12 + 12=-6 + 12\), so \(4x=6\).
Divide both sides by \(4\): \(x=\frac{6}{4}=\frac{3}{2}=1.5\).

Step3: Find the perimeter

Substitute \(x = 1.5\) into the formula for the perimeter of the square \(P = 4(2.5x - 3)\).
\(P=4(2.5\times1.5-3)=4(3.75 - 3)=4\times0.75 = 3\).

Answer:

1. False. The correct equation is \(4(2.5x - 3)=3(2x - 2)\).
2. False. The value of \(x = 1.5\).
3. True.