Question

what is the missing length?
18.2 m
c
area = 126.49 m²

Explanation:

Step1: Recall the area formula for a right triangle

The area \( A \) of a right triangle is given by \( A=\frac{1}{2}\times\text{base}\times\text{height} \). Here, the height is \( 18.2\space m \), the base is \( c \), and the area \( A = 126.49\space m^2 \).

Step2: Substitute the known values into the formula

We substitute \( A = 126.49 \), and height \( = 18.2 \) into the formula \( 126.49=\frac{1}{2}\times c\times18.2 \).
First, simplify the right side: \( \frac{1}{2}\times18.2 = 9.1 \), so the equation becomes \( 126.49 = 9.1\times c \).

Step3: Solve for \( c \)

To find \( c \), we divide both sides of the equation by \( 9.1 \): \( c=\frac{126.49}{9.1} \).
Calculating the division: \( \frac{126.49}{9.1}=13.9 \).

Answer:

The missing length \( c \) is \( 13.9\space m \).