Question

what is the missing length?
14 mi
area = 77 mi²
v = miles

Explanation:

Step1: Recall area formula for triangle

The area \( A \) of a right - triangle is given by \( A=\frac{1}{2}\times base\times height \). In this right - triangle, the base is \( 14\) mi and the height is \( v \) (the unknown side we need to find), and the area \( A = 77\) \( \text{mi}^2 \). So we can write the formula as \( 77=\frac{1}{2}\times14\times v \).

Step2: Simplify the equation

First, simplify \( \frac{1}{2}\times14 \). We know that \( \frac{1}{2}\times14 = 7 \). So the equation becomes \( 77 = 7\times v \).

Step3: Solve for \( v \)

To find \( v \), we divide both sides of the equation \( 77 = 7v \) by \( 7 \). So \( v=\frac{77}{7} \). Calculating \( \frac{77}{7} \), we get \( v = 11 \).

Answer:

\( 11 \)