Question

find the Area of a triangle two sides of which are 15cm and 28cm and the perimeter is 84cm ​

Answer 1

Answer:Let x=the length of the third (non-congruent) side.

x + 3x = 35

4x = 35

x = 35/4. the other sides are (35-35/4)/2 = (105/8)

Step-by-step explanation:

Answer 2

To find the third side, let us take third side = x.

84cm =15cm + 28cm + x

84cm = 43cm + x

84cm - 43cm = x

41 cm = x

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Area of a triangle when its all the sides are

given is :

$\sqrt{s(s - a)( s - b)(s - c)}$

Where, Semiperimeter is calculated by:

$\frac{a + b + c}{2 }$

Using these formulae,

Semiperimeter in this case ;

$\frac{15 + 28 + 41}{2} \: = 42cm$

Area of the triangle :

$\sqrt{42(42 - 15)(42 \: - \: 28)(42 \: - \: 41)}$

$\sqrt{42(27)(14)(1)}$

$\sqrt{2 \times 21(27)(7 \times 2) \times 1}$

$\sqrt{21} \times \sqrt{4} \times \sqrt{27} \times \sqrt{7}$

$2 \times \sqrt{21} \times \sqrt{27} \times \sqrt{7}$

$2 \sqrt{3969} {cm}^{2}$