Question

lesson 1.01 i can solve linear equations using perimeter of polygons
*#1.) in the diagram below ru = 6x, ut = 4x + 4, ts = 5x + 2, and rs = x + 10 and the perimeter is 48 feet.
determine the value of x and the length of all 4 sides; show all work

Explanation:

Step1: Set up perimeter equation

The perimeter of a polygon is the sum of its side - lengths. So, $RU + UT+TS + RS=48$. Substitute the given expressions: $6x+(4x + 4)+(5x + 2)+(x + 10)=48$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $(6x+4x + 5x+x)+(4 + 2+10)=48$, which simplifies to $16x+16 = 48$.

Step3: Isolate the variable term

Subtract 16 from both sides of the equation: $16x+16−16 = 48−16$, resulting in $16x=32$.

Step4: Solve for x

Divide both sides by 16: $\frac{16x}{16}=\frac{32}{16}$, so $x = 2$.

Step5: Find the length of each side

• $RU=6x$, substitute $x = 2$, then $RU=6\times2 = 12$ feet.
• $UT=4x + 4$, substitute $x = 2$, then $UT=4\times2+4=8 + 4=12$ feet.
• $TS=5x + 2$, substitute $x = 2$, then $TS=5\times2+2=10 + 2=12$ feet.
• $RS=x + 10$, substitute $x = 2$, then $RS=2+10 = 12$ feet.

Answer:

$x = 2$; $RU = 12$ feet, $UT = 12$ feet, $TS = 12$ feet, $RS = 12$ feet