The sides of the triangle are 10 cm and 17 cm. Find the height of the triangle, lowered to the base, equal to 21 cm.

1) Find the area on three sides a = 10 cm; h = 17 cm; c = 21 cm: perimeter of the triangle p = (10 + 17 + 21) cm = 48 cm; (p / 2) = 24 cm – we take this value into account in the area formula (p / 2) – half perimeter.

C = √ [24 cm * (24 – 10) cm * (24 – 17) cm * (24 – 21) cm] = √ [(24 cm * 14 cm * 7 cm * 3 cm)] = √ [(7056 ) cm ^ 4] = 84 cm ^ 2.

2) On the other hand, the area of the triangle C = c * h / 2 = 84 cm ^ 2, from where we find the height, pubescent on the base with, and equal to h.

3) h = 2 * C / s = (2 * 84 cm ^ 2) / 21 cm = 8 cm.



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