An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

We analyze the problem using the triangle inequality theorem.
We define x as the length of the congruent legs and set up the inequality 14"> x + x > 14 .
We solve the inequality to find 7"> x > 7 .
The length of one of the congruent legs must be greater than 7 ​ feet.

Explanation

Problem Analysis Let's analyze the problem. We have an isosceles triangle with a base of 14 feet. We need to find the minimum length of the congruent legs such that the triangle is valid. The key here is the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Applying the Triangle Inequality Let x be the length of each of the congruent legs. According to the triangle inequality theorem, we have the following inequalities:

14"> x + x > 14

x"> x + 14 > x

Solving the Inequalities Let's solve the first inequality:


14"> x + x > 14
14"> 2 x > 14
\frac{14}{2}"> x > 2 14 ​
7"> x > 7
The second inequality, x"> x + 14 > x , simplifies to 0"> 14 > 0 , which is always true and doesn't give us any additional restrictions on x .

Final Answer Therefore, the length of one of the congruent legs must be greater than 7 feet. So, the minimum value of x is greater than 7.

Examples
Imagine you are designing a roof for a small cabin. The roof is shaped like an isosceles triangle, and the base of the roof is 14 feet wide. To ensure the roof is structurally sound, you need to determine the minimum length of the two equal sides. Knowing that each side must be greater than 7 feet allows you to choose appropriate materials and design a stable and aesthetically pleasing roof.

Answered by GinnyAnswer | 2025-07-08

To ensure Mr. Anderson's isosceles triangle roof is valid, each of the congruent legs must be greater than 7 feet. This is determined using the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the third. So, x must be greater than 7 feet.
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Answered by Anonymous | 2025-07-23