Question

find the height of the triangle pictured above, if the area is 10 km². round your answer to the nearest tenth. km

Explanation:

Step1: Recall triangle area formula

The area \( A \) of a triangle is given by \( A = \frac{1}{2} \times base \times height \). Let \( h \) be the height, base \( b = 5 \) km, and \( A = 10 \) \( km^2 \).

Step2: Substitute values into formula

Substitute \( A = 10 \), \( b = 5 \) into \( A = \frac{1}{2} \times b \times h \):
\( 10 = \frac{1}{2} \times 5 \times h \)

Step3: Solve for \( h \)

First, simplify the right - hand side: \( \frac{1}{2} \times 5\times h=\frac{5h}{2} \).
Then, solve the equation \( 10=\frac{5h}{2} \) for \( h \). Multiply both sides by 2: \( 20 = 5h \).
Divide both sides by 5: \( h=\frac{20}{5}=4.0 \) (since we need to round to the nearest tenth, and 4 is already a whole number with a tenth place of 0).

Answer:

\( 4.0 \)