Question

find the area of atriangle two
sides of which are 9cm and 5cm
the perimeter is 21cm​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Let the third side of the triangle be ' c '

Given, the two sides of the triangle.

First side (a) = 9cm

Second side (b) = 5cm

The perimeter of triangle = 21cm

⇢ a + b + c = 21

⇢ 9 + 5 + c = 21

⇢ 14 + c = 21

⇢ c = 21 - 14 = 7

∴ The third side of the triangle = 7cm

Semi- perimeter (s) = 21/2 = 10.5cm

Now, let us find the area of the triangle.

$\rm Area \: of \: the\: triangle = \sqrt{s(s-a)(s-b)(s-c)}$

$\rm = \sqrt{10.5(10.5-9)(10.5-5)(10.5 - 7)}$

$\rm = \sqrt{10.5 \times 1.5 \times 5.5 \times 3.5}$

$\rm = \sqrt{303.1875}$

$\rm = 17.41$

∴ Area of the triangle = 17.41cm²