Question

angles and triangles - unit test a
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question 14

1. two sides of a triangle have lengths of 7 ft and 15 ft. which ineq represents the possible length for the third side, x?

a. 8 < x < 22
b. 8 < x < 15
c. 7 < x < 15
d. 8 < x < 7

Explanation:

Step1: Recall Triangle Inequality Theorem

The triangle inequality theorem states that the length of any side of a triangle must be greater than the absolute difference of the other two sides and less than the sum of the other two sides. For a triangle with sides \(a\), \(b\), and \(x\), the inequality is \(|a - b| < x < a + b\).

Step2: Identify the given sides

Here, the two given sides are \(a = 7\) ft and \(b = 15\) ft.

Step3: Calculate the difference and sum

First, find the absolute difference: \(|15 - 7| = 8\). Then, find the sum: \(15 + 7 = 22\).

Step4: Apply the inequality

Using the triangle inequality theorem, the length of the third side \(x\) must satisfy \(8 < x < 22\).

Answer:

A. \(8 < x < 22\)