Question

1. if △jkl is an equilateral triangle. if qr is seven less than twice x, rs is 61 less than five times x, and qs is 11 more than x, find the value of x and the measure of each side.
2. △qrs is an equilateral triangle. if qr is seven less than twice x, rs is 61 less than five times x, and qs is 11 more than x, find the value of x and the measure of each side.

Explanation:

Step1: Set up the equation

Since $\triangle QRS$ is equilateral, $QR = RS=QS$. We know that $QR = 2x - 7$, $RS=5x - 61$, and $QS=x + 11$. Set $QR = QS$. So, $2x-7=x + 11$.

Step2: Solve for $x$

Subtract $x$ from both sides of the equation $2x-7=x + 11$: $2x-x-7=x - x+ 11$, which simplifies to $x-7 = 11$. Then add 7 to both sides: $x-7 + 7=11 + 7$, so $x = 18$.

Step3: Find the measure of each side

Substitute $x = 18$ into the expression for $QS$ (we could use any of the side - length expressions). $QS=x + 11=18 + 11=29$.

Answer:

$x = 18$, measure of each side is 29