Question

assignment #8 - isosceles and equilateral triangles
find the length of each side.
rp=
pq=
rq=

Explanation:

Step1: Set up the equation

Since \(RP = RQ\) (marked as equal in the isosceles triangle), we have \(4x - 3=2x + 9\).
Subtract \(2x\) from both sides: \(4x-2x - 3=2x-2x + 9\), which simplifies to \(2x-3 = 9\).
Add \(3\) to both sides: \(2x-3 + 3=9 + 3\), so \(2x=12\).
Divide both sides by \(2\): \(x=\frac{12}{2}=6\).

Step2: Find \(RP\)

Substitute \(x = 6\) into \(RP=4x - 3\).
\(RP=4\times6-3=24 - 3=21\).

Step3: Find \(PQ\)

Substitute \(x = 6\) into \(PQ = 3x+2\).
\(PQ=3\times6+2=18 + 2=20\).

Step4: Find \(RQ\)

Substitute \(x = 6\) into \(RQ=2x + 9\).
\(RQ=2\times6+9=12 + 9=21\).

Answer:

\(RP = 21\)
\(PQ=20\)
\(RQ = 21\)