Question

b. 1 mile = 5,280
d. 1 ________________ = 7 days
f. 1 ________________ = about 52 weeks
h. 1 ________________ = 1,760 yards
draw the shape.
b. draw a triangle with one 3-inch line, one 2-inch line, and one other line. how long is the third line? ________________

Explanation:

Step1: Recall Triangle Inequality

For a triangle with sides \(a\), \(b\), \(c\), the triangle inequality states \(|a - b| < c < a + b\). Here, \(a = 3\) inches, \(b = 2\) inches.

Step2: Calculate Bounds

Lower bound: \(|3 - 2| = 1\) inch. Upper bound: \(3 + 2 = 5\) inches. So the third side must be between \(1\) inch and \(5\) inches (not including \(1\) and \(5\) for a non - degenerate triangle). If we assume it's a valid triangle (e.g., a scalene or isoceles triangle with integer length for simplicity, a common case could be \(2\) inches (isoceles) or \(3\) inches, but more generally, any length \(l\) where \(1 < l < 5\). However, if we consider a right - triangle (though not specified), using Pythagoras: if \(3\) and \(2\) are legs, \(c=\sqrt{3^{2}+2^{2}}=\sqrt{9 + 4}=\sqrt{13}\approx3.6\) inches; if \(3\) is hypotenuse, \(c=\sqrt{3^{2}-2^{2}}=\sqrt{9 - 4}=\sqrt{5}\approx2.2\) inches. But since the problem just says "draw a triangle" without specifying type, the key is the triangle inequality. A common answer (if we take integer and simple) could be between \(1\) and \(5\) inches, for example, \(2\) or \(3\) inches (but strictly by inequality, it's \(1 < x < 5\)).

Answer:

The length of the third line is between \(1\) inch and \(5\) inches (e.g., \(2\) inches, \(3\) inches, \(3.6\) inches depending on triangle type). If we assume a simple non - right triangle with integer lengths, a possible answer is \(2\) inches (or other values in \((1,5)\)).