Question

what is the missing length?
4 mi
v
area = 11.6 mi²

Explanation:

Step1: Recall triangle area formula

The area of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). Here, the height \( h = 4 \) mi, area \( A = 11.6 \) \( \text{mi}^2 \), and the base is \( v \) (the missing length we need to find).

Step2: Substitute values into formula

Substitute \( A = 11.6 \), \( h = 4 \) into \( A = \frac{1}{2} \times v \times h \):
\( 11.6 = \frac{1}{2} \times v \times 4 \)

Step3: Simplify and solve for \( v \)

Simplify the right - hand side: \( \frac{1}{2} \times 4\times v=2v \). So the equation becomes \( 11.6 = 2v \).
Divide both sides by 2: \( v=\frac{11.6}{2}=5.8 \)

Answer:

The missing length \( v \) is \( 5.8 \) miles.