Question

point s is on line segment $overline{rt}$. given $st = 3x - 8$, $rt = 4x$, and $rs = 4x - 7$, determine the numerical length of $overline{rt}$. answer attempt 1 out of 2 $rt=$

Explanation:

Step1: Use segment - addition postulate

Since point S is on line segment $\overline{RT}$, we have $RS + ST=RT$. Substitute the given expressions: $(4x - 7)+(3x - 8)=4x$.

Step2: Simplify the left - hand side

Combine like terms: $4x+3x-7 - 8 = 4x$, which simplifies to $7x-15 = 4x$.

Step3: Solve for x

Subtract $4x$ from both sides: $7x-4x-15=4x - 4x$, getting $3x-15 = 0$. Then add 15 to both sides: $3x=15$. Divide both sides by 3: $x = 5$.

Step4: Find the length of RT

Since $RT = 4x$, substitute $x = 5$ into the expression. So $RT=4\times5=20$.

Answer:

$20$