Question

find the area of a triangle whose sides are 8 cm and 11 cm and the perimeter is 32 cm?
step by step​

Answer 1

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let the sides of the triangle be a, b and c

given length of the sides of the triangle are :-

a = 8cm

b = 11cm

c = ?

perimeter of the triangle is given = 32cm

since the sum of all three sides of a triangle is it's perimeter

=> a + b + c = 32cm

=> 8 + 11 + c = 32cm

=> 19 + c = 32cm

=> c = 32 - 19

=> c = 13cm

now we will find the area of the triangle by heron's formula which is √s(s-a)(s-b)(s-c) where s is the semi-perimeter of the triangle.

semi-perimeter of this triangle = 32/2

= 16cm

area of the triangle = √16(16-8)(16-11)(16-13)

= √(16 × 8 × 5 × 3)

= √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 3)

= 2 × 2 × 2√(2 × 5 × 3)

= 8√30cm²

Answer 2

Answer:

third side of the triangle={32-(8+11)}cm

=13cm

half of the perimeter is 32/2cm=16cm

so the area of the triangle is

√16(16-8)(16-11)(16-13)sqcm

=√16.8.5.3sqcm

=8√30sqcm