Question

an isosceles triangle has two congruent sides, called legs. the third side is called the base. an isosceles triangle has a base of 5 cm and a perimeter of 27 cm. what is the length of each leg of the triangle? answer with supporting work:

Explanation:

Step1: Recall perimeter formula

The perimeter \(P\) of a triangle is \(P = a + b+ c\). In an isosceles triangle with base \(b\) and two equal legs \(a\), \(P=2a + b\).

Step2: Substitute known values

We know \(P = 27\) cm and \(b = 5\) cm. Substituting into \(P=2a + b\) gives \(27=2a + 5\).

Step3: Solve for \(a\)

First, subtract 5 from both sides of the equation: \(27−5=2a+5 - 5\), so \(22 = 2a\). Then divide both sides by 2: \(\frac{22}{2}=a\), so \(a = 11\) cm.

Answer:

11 cm