Question

find area of triangle with sides 15 cm , 14 cm and perimeter 42 cm​

Answer 1

Given:-

→Two sides of a triangle = 15cm,14cm

→Perimeter of the triangle = 42cm

To find:-

•Area of the triangle

Solution:-

Firstly,let's find the 3rd side of the triangle.

Let the 3rd side of the triangle be x.

Perimeter of a triangle = Sum of 3 sides

=>15+14+x = 42

=>29 + x = 42

=>x = 42-29

=>x = 13cm

Thus,3rd side of the triangle is 13cm.

Hence:-

=> a = 15cm

=> b = 14cm

=> c = 13cm

Now,semi-perimeter(s) of the triangle:-

=>42/2

=>21cm

Hence,

=>s = 21cm

=>(s-a) = (21-15) = 6cm

=>(s-b) = (21-14) = 7cm

=>(s-c) = (21-13) = 8cm

Now,according to Heron's formula ,area of the given triangle is :-

=> ∆ = √s(s-a)(s-b)(s-c)

=√21×6×7×8

=√7056

= 84cm²

Thus,area of the triangle is 84cm².

Answer 2

Given:

sides of ️ = 15 cm and 14 cm

perimeter = 42 cm

To find:

Third side of triangle = ?

Area of triangle = ?

Solution:

:. Primeter = a + b + c

let the third side be = x

=> 15 + 14 + x = 42

=> 29 + x = 42

=> x = 42 - 29

=> x = 13 cm

So, third side is 13 cm

Area of a triangle is given by = under root s (s-a)(s-b)(s-c)

here, s is the semi-perimeter i.e, a+b+c/2

--> s = 15 + 14 + 13/2

--> s = 21 cm

so, the area will be = root 21×(21-15)(21-14)(21-13)

=> root 3 × 7 × 6 × 7 × 8

=> root 3 × 7 × 3 × 2 × 7 × 4 × 2

=> 3 × 7 × 2 × 2

=> 21 × 4

=> 84 cm^2

hence, we get the required ans

hope this helped you dear...