Question

what is the missing length?
4 in
area = 14 in²
v = inches

Explanation:

Step1: Recall area formula for triangle

The area \( A \) of a right - triangle (or any triangle) is given by the formula \( A=\frac{1}{2}\times base\times height \). In this right - triangle, the base is \( 4 \) inches and the height is \( v \) inches, and the area \( A = 14\space in^{2}\).

Step2: Substitute values into the formula

Substitute \( A = 14 \), \( base = 4 \) into the formula \( A=\frac{1}{2}\times base\times height \). We get \( 14=\frac{1}{2}\times4\times v \).
First, simplify the right - hand side: \( \frac{1}{2}\times4 = 2 \), so the equation becomes \( 14 = 2\times v \).

Step3: Solve for \( v \)

To solve for \( v \), we divide both sides of the equation \( 14 = 2v \) by \( 2 \). So \( v=\frac{14}{2}=7 \).

Answer:

\( 7 \)