Question

Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is
42cm​

Answer 1

Answer:

2(18+19)

2×37

= 74. .......

Answer 2

side 1 = 18 cm

side 2 = 10 cm

side 3 = ?

perimeter = 42 cm

side 3 = perimeter - ( side 1 + side 2 )

side 3 = 42 - ( 18 + 10 )

side 3 = 42 - 28

side 3 = 14 cm

area of triangle through heron's formula.

heron's formula =

√s(s-a)(s-b)(s-c)

where,

s = semi perimeter

a = side 1

b = side 2

c = side 3

semi perimeter = 42/2 = 21 cm

procedure for solving

√s(s-a)(s-b)(s-c)

= √21 (21-18) (21-10) (21-14)

= √21 × 3 × 11 × 7

= √3 × 7 × 3 × 11 × 7

= √3 × 3 × 7 × 7 × 11 { regrouping }

= 3√7 × 7 × 11

= 21√11 cm²

Therefore, the area of the triangle is 21√11 cm²