Question

1. point s is between r and t on rt. use the given information to draw a picture and write an equation in terms of x. solve the equation. then find rs and st. rs = 3x - 16 mm, st = 4x - 8 mm, rt = 60 mm. x = _, rs = _, st = ___

Explanation:

Step1: Set up the equation

Since point S is between R and T, we have $RS + ST=RT$. Substituting the given expressions, we get $(3x - 16)+(4x - 8)=60$.

Step2: Combine like - terms

Combining the x - terms and the constant terms on the left - hand side, we have $(3x+4x)+(-16 - 8)=60$, which simplifies to $7x-24 = 60$.

Step3: Isolate the variable term

Add 24 to both sides of the equation: $7x-24 + 24=60 + 24$, resulting in $7x=84$.

Step4: Solve for x

Divide both sides of the equation by 7: $\frac{7x}{7}=\frac{84}{7}$, so $x = 12$.

Step5: Find RS

Substitute $x = 12$ into the expression for RS: $RS=3x-16=3\times12 - 16=36 - 16=20$ mm.

Step6: Find ST

Substitute $x = 12$ into the expression for ST: $ST=4x-8=4\times12 - 8=48 - 8=40$ mm.

Answer:

$x = 12$, $RS = 20$ mm, $ST = 40$ mm