Question

An triangle has perimeter 32 cm and two sides of which are 8 cm and 11 cm. Find

the area of the triangle.​

Answer 1

Answer:

8√30cm²

Step-by-step explanation:

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

Step-by-step explanation:

Third side = 32-(8+11) = 32-19 = 13

Area of triangle

=

$semi \: perimeter \: \\ = \frac{8 + 11 + 13}{2} = \frac{32}{2} = 16cm \\ \\ area = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{16(16 - 8)(16 - 11)(16 - 13)} \\ = \sqrt{16 \times 8 \times 5 \times 3} \\ = \sqrt{4 \times 4 \times 2 \times 2 \times 2 \times 5 \times 3} \\ 8 \sqrt{30} cm$