Question

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

Answer 1

Solution:

Assume the third side of the triangle to be “x”.

Now, the three sides of the triangle are 18 cm, 10 cm, and “x” cm

It is given that the perimeter of the triangle = 42cm

So, x = 42 – (18 + 10) cm = 14 cm

∴ The semi perimeter of triangle = 42/2 = 21 cm

Using Heron’s formula,

Area of the triangle,

= √[s (s-a) (s-b) (s-c)]

= √[21(21 – 18) (21 – 10) (21 – 14)] cm2

= √[21 × 3 × 11 × 7] m2

= 21√11 cm2

______________________

Hope it will be helpful :)

Answer 2

Solution :

Assume the three sides of the triangle be "x".

Now,

the sides of the triangle are 18cm, 10cm and "x"cm.

Given,

the perimeter of the triangle =42cm

so,

42=x+18+10

42=x+28

x=42-28

x=14cm

The semi perimeter of the triangle =21cm

USING HERONS FORMULA,

s=21cm

a=18cm

b=10cm

c=14cm

Area of the triangle

=√[s(s-a)(s-b)(s-c)]

=√[21(21-18)(21-10)(21-14)]

=√21×3×11×7

=√21×21×11

=21√11

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