Question

11/7 - isosceles and equilateral practice
determine the value of x and y.
perimeter is 54.
x=
y=

Explanation:

Step1: Determine the type of triangle

Since two angles are \(60^{\circ}\), the third angle \(y = 60^{\circ}\) (sum of angles in a triangle is \(180^{\circ}\), \(y=180 - 60 - 60\)). So it's an equilateral triangle (all angles \(60^{\circ}\)).

Step2: Use perimeter formula

In an equilateral triangle, all sides are equal. Let side length be \(4x\). Perimeter \(P=3\times4x\). Given \(P = 54\), so \(3\times4x=54\).

Step3: Solve for \(x\)

\(12x = 54\), then \(x=\frac{54}{12}=\frac{9}{2}=4.5\)

Answer:

\(x = 4.5\), \(y = 60\)