Question

what is the missing length?
4.5 mi
area of shaded region = 9 mi²
t = \boxed{} miles

Explanation:

Step1: Recall the area formula for a triangle

The area \( A \) of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). Here, the height is \( 4.5 \) mi, the base is \( t \), and the area is \( 9 \) \( \text{mi}^2 \).

Step2: Substitute the known values into the formula

Substitute \( A = 9 \), height \( = 4.5 \) into \( A = \frac{1}{2} \times \text{base} \times \text{height} \):
\( 9 = \frac{1}{2} \times t \times 4.5 \)

Step3: Solve for \( t \)

First, simplify the right - hand side: \( \frac{1}{2} \times 4.5=\frac{4.5}{2} = 2.25 \)
So the equation becomes \( 9 = 2.25t \)
Then, divide both sides by \( 2.25 \) to solve for \( t \): \( t=\frac{9}{2.25} \)
\( \frac{9}{2.25}=\frac{9\times100}{2.25\times100}=\frac{900}{225} = 4 \)

Answer:

\( t = 4 \) miles