Q.

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

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Detailed Solution

We know that, 

The Heron's formula for calculating the area of the triangle,

Area of triangle = s (s - a) (s - b) (s -c)

where, s is the semi-perimeter = half of the perimeter = 21 cm

and  a, b and c are the sides of the triangle 

Triangular sides of walls are, a = 18 cm, b = 10 cm, c = ?

Thus, Semi-perimeter 

s = (a + b + c)/2

21 = (18 + 10 + c)/2

21 × 2 = 28+ c

42 = 28 +c

c =  14 cm

Area of a triangular wall = s (s - a) (s - b) (s -c)

21(21 - 18)(21 - 10)(21 - 14)

21 × 3 × 11 × 7

= 2111  cm2

Hence, Area of the wall of the park to be painted in colour = 21 11cm2.

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