Question

reasoning you are bending a strip of metal into an isosceles triangle for a sculpture. the strip of metal is 20 inches long. the first bend is made 6 inches from one end. describe two ways you could complete the triangle.

Explanation:

Step1: Consider the first case where the 6 - inch side is one of the equal sides

Let the equal sides be \(a = 6\) inches. The perimeter \(P=a + a + b\), where \(P = 20\) inches. Substitute \(a = 6\) into the perimeter formula: \(20=6 + 6 + b\).

$$b=20-(6 + 6)=8$$

Check the triangle inequality: \(6+6>8\), \(6 + 8>6\), \(8+6>6\)

Step2: Consider the second case where the 6 - inch side is the base

Let the base \(b = 6\) inches. The perimeter \(P=a + a + b\), where \(P = 20\) inches. Substitute \(b = 6\) into the perimeter formula: \(20=a + a+6\).

$$2a=20 - 6=14$$

$$a = 7$$

Check the triangle inequality: \(7+7>6\), \(7 + 6>7\), \(6+7>7\)

Answer:

One way: The triangle has side lengths \(6\) inches, \(6\) inches, and \(8\) inches. Another way: The triangle has side lengths \(7\) inches, \(7\) inches, and \(6\) inches.