Question

Sides of a triangle are in the ratio 13:14:15 and its perimeter is 84 cm. Find its area, find its area using heron's formula.
answer with step-by-step explanation​

Answer 1

Answer:

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Step-by-step explanation:

Let the sides of the triangle be 13a,14a,15a.

Perimeter of the triangle = Sum of all sides =13a+14a+15a=42a

Given, perimeter of the triangle =84cm

∴42a=84cm

a=2cm

So, the sides of the triangle are 13a=26cm,14a=28cm,15a=30cm.

Area of triangle with sides a, b, and c and s=2a+b+c is s(s−a)(s−b)(s−c). 

For triangle with sides 26  cm, 28  cm and 30  cm, s=226+28+30=42cm

Area of the triangle with 26  cm, 28  cm and 30  cm =42(42−26)(42−28)(42−30)

=42×16×14×12

=6×7×4×4×7×2×6×2

=6×7×4×2=336cm2

Answer 2

Step-by-step explanation:

Let the sides of the triangle be 13a,14a,15a.

Perimeter of the triangle = Sum of all sides =13a+14a+15a=42a

Given, perimeter of the triangle =84cm

∴42a=84cm

a=2cm

So, the sides of the triangle are 13a=26cm,14a=28cm,15a=30cm.

Area of triangle with sides a, b, and c and s=2a+b+c is s(s−a)(s−b)(s−c). 

For triangle with sides 26  cm, 28  cm and 30  cm, s=226+28+30=42cm

Area of the triangle with 26  cm, 28  cm and 30  cm =42(42−26)(42−28)(42−30)

=42×16×14×12

=6×7×4×4×7×2×6×2

=6×7×4×2=336cm2