Question

in △rst, if s=t, rs = 9x - 13, st = 10x - 3, and rt = 4x + 2, find x and the measure of each side. rt= st= rs= x=

Explanation:

Step1: Set up equation using equal - side property

Since \(S = T\), then \(RS=RT\). So, \(9x - 13=4x + 2\).

Step2: Solve for \(x\)

Subtract \(4x\) from both sides: \(9x-4x - 13=4x-4x + 2\), which simplifies to \(5x-13 = 2\). Then add 13 to both sides: \(5x-13 + 13=2 + 13\), getting \(5x=15\). Divide both sides by 5: \(x=\frac{15}{5}=3\).

Step3: Find the length of \(RS\)

Substitute \(x = 3\) into the expression for \(RS\): \(RS=9x-13=9\times3-13=27 - 13 = 14\).

Step4: Find the length of \(ST\)

Substitute \(x = 3\) into the expression for \(ST\): \(ST=10x-3=10\times3-3=30 - 3=27\).

Step5: Find the length of \(RT\)

Substitute \(x = 3\) into the expression for \(RT\): \(RT=4x + 2=4\times3+2=12 + 2=14\).

Answer:

\(x = 3\), \(RS=14\), \(ST=27\), \(RT=14\)