Question

1. △qrs is an equilateral triangle. if qr is seventeen more than twice x, rs is 19 less than six times x, and qs is one less than four times x, find x and the measure of each side.

x =
qr =
rs =
qs =

Explanation:

Step1: Write expressions for each side

Since $\triangle QRS$ is equilateral, $QR = RS=QS$. Given $QR = 2x + 17$, $RS=6x - 19$, and $QS = 4x-1$.

Step2: Set up an equation using two - equal sides

Set $QR = RS$. So, $2x + 17=6x - 19$.

Step3: Solve the equation for x

Subtract $2x$ from both sides: $17 = 4x-19$. Then add 19 to both sides: $17 + 19=4x$, which gives $36 = 4x$. Divide both sides by 4, we get $x = 9$.

Step4: Find the length of each side

Substitute $x = 9$ into the expression for $QR$ (we could use any of the side - length expressions). $QR=2x + 17=2\times9 + 17=18 + 17 = 35$. Since $QR = RS = QS$, $RS = 35$ and $QS = 35$.

Answer:

$x = 9$, $QR=35$, $RS = 35$, $QS = 35$