Question
Download Solution PDFTriangle DEF is an equilateral triangle with a side length of 12 cm. If point G is the mid point of side DE, what is the length (in cm) of side FG?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Triangle DEF is an equilateral triangle with a side length of 12 cm.
Point G is the midpoint of side DE.
Formula Used:
In an equilateral triangle, the length of the median is calculated using the formula:
\(Median = \frac{\sqrt{3}}{2} \times \text{side length}\)
Calculation:
Since G is the midpoint of DE, DG = GE = 6 cm.
In an equilateral triangle, the median also acts as the altitude. Let's calculate FG, where F is the vertex opposite to DE.
Using the median formula:
Median = \(\frac{\sqrt{3}}{2} \times 12\)
⇒ Median = \(\frac{\sqrt{3}}{2} \times 12 = 6\sqrt{3}\)
The length of side FG is 6√3 cm.
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