In an isosceles triangle, the side is 10 cm and the base is 12 cm. What is the height lowered to the base?

univerkov | March 2, 2021 | education

1. Triangle ABC – isosceles => AB = BC; ВO – height, ABC – isosceles => BO – median, bisector (by the property of an isosceles triangle) => AO = OC => AO = AC / 2 = 12/2 = 6 cm. 2. ВO – height => AOB = BOC = 90 degrees => triangle AOB – rectangular => AO ^ 2 + BO ^ 2 = AB ^ 2; BO ^ 2 = AB ^ 2 – AO ^ 2; BO = √ (AB ^ 2 – AO ^ 2); BO = √ (10 ^ 2 – 6 ^ 2) = √ (100 – 36) = √64 = 8 cm.
Answer: 8 centimeters.

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