Question

find the missing side of each triangle. round your answers to the nearest tenth if necessary.
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1. two sides of a triangle have the following measures, 6 and 17. find the range of possible measures for the third side.

a) 6 < x < 23 b) -11 < x < 11
c) 11 < x < 23 d) 11 < x < 17

1. which equation represents a line that is parallel to the line y=1/2x-3

a) y=2x-3 b) y=1/2x-2
c) y= -1/2x-3 d) y=2x+4

1. which equation represents a line that is perpendicular to the line y= -1/4x+5.

a) y=4x-2 b) y= -1/4x+4
c) y=1/4x-6 d) y=-4x+5

1. what is the equation for a perpendicular line to the previous problem.

a) y=(2/3)x-1 b) y=(-3/2)x+1
c) y=(3/2)x-1 d) y=(-2/3)x+1
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Explanation:

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Step1: Identify triangle type

It's a right triangle, so use Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c = 13\), \(b = 12\), find \(a = x\).

Step2: Apply Pythagorean theorem

\(x^2 + 12^2 = 13^2\)
\(x^2 + 144 = 169\)
\(x^2 = 169 - 144 = 25\)
\(x = \sqrt{25} = 5\)

Step1: Identify triangle type

Right triangle, use Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a = 12\), \(b = 5\), find \(c = x\).

Step2: Apply Pythagorean theorem

\(x^2 = 12^2 + 5^2\)
\(x^2 = 144 + 25 = 169\)
\(x = \sqrt{169} = 13\)

Step1: Recall triangle inequality

For a triangle with sides \(a\), \(b\), \(c\), \(|a - b| < c < a + b\). Here \(a = 17\), \(b = 6\).

Step2: Calculate range

\(|17 - 6| < x < 17 + 6\)
\(11 < x < 23\)

Answer:

\(5\) m

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