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

| September 23, 2021 | education

In this problem, we have three sides of a triangle, which we denote as a = 10 cm, b = 17 cm,

c = 21 cm.In order to find the height h lowered to the base c = 21 cm, we use

formulas for the area of ​​a triangle: Heron’s formula and the formula through the height and base.

According to Heron’s formula, we can calculate the area of ​​a triangle, first finding p –

semi-perimeter p = (a + b + c): 2 = (10 + 17 + 21): 2 = 48: 2 = 24 (cm).

And by inserting all the data, we get according to Heron’s formula S = square root of the product

p * (p – a) * (p – b) * (p – c) or

S = square root of product 24 * (24 – 10) * (24 – 17) * (24 – 21)

Hence S = 84 square cm. Now we will use the second formula for the area of ​​a triangle,

where S = (h * c) / 2 that is 84 = (h * 21) / 2 or 168 = h * 21, then we find

h = 8 cm.



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