Question

what is the missing length? 18 in area = 198 in² v = ____ inches

Explanation:

Step1: Recall area formula for triangle

The area \( A \) of a right - triangle is given by \( A=\frac{1}{2}\times base\times height \). Here, the base is \( 18 \) inches, the height is \( v \) (the missing length), and the area \( A = 198\space in^{2}\). So we have the formula \( 198=\frac{1}{2}\times18\times v \).

Step2: Simplify the right - hand side

First, calculate \( \frac{1}{2}\times18 \). \( \frac{1}{2}\times18 = 9 \). So the equation becomes \( 198 = 9\times v \).

Step3: Solve for \( v \)

To find \( v \), we divide both sides of the equation \( 198 = 9v \) by \( 9 \). So \( v=\frac{198}{9} \).

Step4: Calculate the value of \( v \)

\( \frac{198}{9}=22 \).

Answer:

22