Question

The side of a triangles are 8cm,12cm,17cm.find its perimeter and its are by using herons formula

Answer 1

Hi!

Heron's formula:

`s = (a+b+c)/(2)`

Area =
`√(s(s-a)(s-b)(s-c))`

Perimeter = 8 + 12 + 17 = 37 cm

`s = (37)/(2) = 18.5`

Area =
`√(18.5(18.5-8)(18.5-12)(18.5-17)) = √(18.5 * 10.5 * 6.5 * 1.5) = √(1893,9375)`

[tex]\sqrt{1893.9375} ≈ 43.52

Area ≈ 43.52 cm²

Wish Good Lessons! ^-^

Answer 2

see explanation

Explanation:

The perimeter is the sum of the 3 sides, that is

perimeter = 8 + 12 + 17 = 37 cm

To use Heron's formula for area (A)

A =
`√(s(s-a)(s-b)(s-c))`

where a, b and c are the lengths of sides and s the semi perimeter

s = 37 ÷ 2 = 18.5

let a = 8, b = 12 and c = 17, then

A =
`√(18.5(18.5-8)(18.5-12)(18.5-17))`

=
`√(18.5(10.5)(6.5)(1.5))`

=
`√(1893.9375)` ≈ 43.52 cm² ( to 2 dec. places )