Question

isosceles triangles
triangle abc is equilateral. \\( \overline { b d } \\) bisects \\( \angle a b c \\). the length of \\( \overline { a d } \\) is \\( ( 5 x + 1 ) \\) feet, and the length
of \\( \overline { b c } \\) is 60 feet. what is the value of \\( x? \\)
enter your answer in the box.
\\( x = \\)

Explanation:

Step1: Use the property of an equilateral triangle

In an equilateral triangle, the angle - bisector, median, and altitude coincide. Since \(BD\) bisects \(\angle ABC\) in equilateral \(\triangle ABC\), \(AD=\frac{1}{2}AC\). And in an equilateral triangle \(AC = BC\). Given \(BC = 60\) feet, then \(AC=60\) feet. So \(AD=\frac{1}{2}\times60 = 30\) feet.

Step2: Solve the equation for \(x\)

We know that \(AD=(5x + 1)\) feet and \(AD = 30\) feet. So we set up the equation \(5x+1=30\).
Subtract \(1\) from both sides: \(5x=30 - 1=29\).
Divide both sides by \(5\): \(x=\frac{29}{5}=5.8\).

Answer:

\(5.8\)