Question

in the diagram, rt = 59. what are rs and st? 8x - 14 4x + 1 r s t

Explanation:

Step1: Set up equation

Since $RT = RS+ST$, we have $(8x - 14)+(4x + 1)=59$.
Combining like - terms, we get $8x+4x-14 + 1=59$, which simplifies to $12x-13 = 59$.

Step2: Solve for x

Add 13 to both sides of the equation: $12x-13 + 13=59 + 13$, so $12x=72$.
Divide both sides by 12: $\frac{12x}{12}=\frac{72}{12}$, then $x = 6$.

Step3: Find RS

Substitute $x = 6$ into the expression for $RS$: $RS=8x-14=8\times6-14=48 - 14=34$.

Step4: Find ST

Substitute $x = 6$ into the expression for $ST$: $ST=4x + 1=4\times6+1=24 + 1=25$.

Answer:

$RS = 34$, $ST = 25$