Question

the triangle shown is isosceles. find the length of each side and the perimeter. (5n - 17) cm (2n + 1) cm n cm each of the two congruent sides has length □ □ the third side has length □ □ (type integers or decimals.)

Explanation:

Step1: Set congruent sides equal

In an isosceles triangle, the two congruent sides are \(5n - 17\) and \(2n + 1\). So, \(5n - 17 = 2n + 1\).

Step2: Solve for n

Subtract \(2n\) from both sides: \(3n - 17 = 1\). Add 17 to both sides: \(3n = 18\). Divide by 3: \(n = 6\).

Step3: Find congruent side length

Substitute \(n = 6\) into \(2n + 1\): \(2(6)+1 = 13\) cm. (Same as \(5(6)-17 = 13\) cm)

Step4: Find third side length

Third side is \(n = 6\) cm.

Step5: Calculate perimeter

Perimeter = \(13 + 13 + 6 = 32\) cm.

Answer:

Each of the two congruent sides has length \(13\) cm. The third side has length \(6\) cm. The perimeter is \(32\) cm.