Question

find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 24 cm.
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Answer 1

Question :

Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 24cm

Answer:

Let a,b,c be the sides of a triangle.

Perimeter = 42cm

a + b + c = 42 ....(1)

Also given, a = 18 and b = 10

Putting the value of a and b in equation 1

18 + 10 + c = 42

28 + c = 42

c = 42 - 28

c = 14

Now putting the value of a, b and c in the formula,

Area of triangle = $\sqrt[]{s(s - a)(s - b(s - c)}$

where, $s = \frac{a + b + c}{2} = 21cm$

Area of triangle = $\sqrt{21(21 - 18)(21 - 10)(21 - 14)}$

$= 69.69 {cm}^{2}$

Hence, the area of triangle is 69.69cm²