Question

1. $\triangle wxy$ is an isosceles triangle with $\overline{wx} \cong \overline{wy}$. if wx is 3 more than four times x, xy is 7 less than five times x, and wy is 66 less than seven times x, find x and the measure of each side.

Explanation:

Step1: Express the sides in terms of \(x\)

Given \(WX = 4x + 3\), \(XY=5x - 7\), \(WY = 7x-66\)
Since \(\overline{WX}\cong\overline{WY}\) (isosceles triangle property), we set up the equation \(4x + 3=7x - 66\)

Step2: Solve for \(x\)

Subtract \(4x\) from both sides: \(3 = 3x-66\)
Add \(66\) to both sides: \(3 + 66=3x\), so \(69 = 3x\)
Divide both sides by \(3\): \(x = 23\)

Step3: Find the length of each side

• For \(WX\): Substitute \(x = 23\) into \(WX=4x + 3\), \(WX=4\times23+3=92 + 3=95\)
• For \(WY\): Since \(WX\cong WY\), \(WY = 95\)
• For \(XY\): Substitute \(x = 23\) into \(XY = 5x-7\), \(XY=5\times23-7=115 - 7 = 108\)

Answer:

\(x = 23\), \(WX = 95\), \(WY = 95\), \(XY = 108\)