what is the approximate value of b, rounded to the nearest tenth?\n7.2 units\n7.8 units\n8.6 units\n9.4 units

Explanation:

Step1: Use the geometric - mean theorem

In a right - triangle, if an altitude is drawn to the hypotenuse, then the following relationships hold. We can use the fact that (b^{2}=a\times(a + 5)). First, find (a) using the geometric - mean relationship in the smaller right - triangles. We know that (6^{2}=a\times5), so (a=\frac{36}{5}=7.2).

Step2: Calculate (b)

Now that (a = 7.2), we use the formula (b^{2}=a\times(a + 5)). Substitute (a = 7.2) into the formula: (b^{2}=7.2\times(7.2 + 5)=7.2\times12.2 = 87.84). Then (b=\sqrt{87.84}\approx9.4).

Answer:

9.4 units