The area of the isosceles triangle ABC with the base of the AC is 4800 cm2. Find the heights drawn to the sides of the triangle if AB = 100cm.
1. Vertices of triangle A, B, C. CE and AK – heights. AB = BC = 100 centimeters.
2. We calculate the length of the height CE, using the formula for calculating the area (S) of a given triangle:
S = AB x CE / 2 = 100 x CE / 2 = 4800 centimeters².
CE = 2S / 100 = 2 x 4800/100 = 96 centimeters.
3. We calculate the length of the height of the AK using another formula for calculating the area of a triangle:
S = BC x AK / 2.
AK = 2S / BC = 2 x 4800/100 = 96 centimeters.
Answer: AK = CE = 96 centimeters.
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