Question

the perimeter of the triangle below is equal to 4(x + 5). it write an equation for its perimeter, then solve for x in the space provided below.
a. write a correct equation and solve it. show all your steps.
b. use the value of \x\ to solve for the missing side lengths
x=
2x + 4=
3x - 4=

Explanation:

Step1: Write the perimeter formula

The perimeter \(P\) of a triangle is the sum of its side lengths. So \(P=x+(2x + 4)+(3x-4)\). And we know \(P = 4(x + 5)\). Then the equation is \(x+(2x + 4)+(3x-4)=4(x + 5)\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+2x + 3x)+(4 - 4)=6x\). The right - hand side is \(4x+20\). So the equation becomes \(6x=4x + 20\).

Step3: Solve for \(x\)

Subtract \(4x\) from both sides: \(6x-4x=4x + 20-4x\), which gives \(2x=20\). Then divide both sides by \(2\): \(x=\frac{20}{2}=10\).

Step4: Find the side lengths

For \(2x + 4\), substitute \(x = 10\): \(2\times10+4=20 + 4=24\).
For \(3x-4\), substitute \(x = 10\): \(3\times10-4=30-4=26\).

Answer:

a. The equation is \(x+(2x + 4)+(3x-4)=4(x + 5)\) and \(x = 10\).
b. \(x = 10\), \(2x+4=24\), \(3x - 4=26\)