Question

a triangle has an area of 100 square kilometers and a base of 12.5 kilometers. what is the height?
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Explanation:

Step1: Recall the area formula for a triangle

The area \( A \) of a triangle is given by the formula \( A=\frac{1}{2} \times \text{base} \times \text{height} \), which can be rewritten as \( A = \frac{1}{2}bh \), where \( b \) is the base and \( h \) is the height. We need to solve for \( h \), so we can rearrange the formula. Multiply both sides of the equation by 2: \( 2A=bh \). Then divide both sides by \( b \) to get \( h=\frac{2A}{b} \).

Step2: Substitute the given values into the formula

We know that the area \( A = 100 \) square kilometers and the base \( b = 12.5 \) kilometers. Substitute these values into the formula for \( h \): \( h=\frac{2\times100}{12.5} \).

Step3: Perform the calculation

First, calculate the numerator: \( 2\times100 = 200 \). Then divide 200 by 12.5: \( \frac{200}{12.5}=16 \).

Answer:

16