Question

5. What is the area of a
triangle whose two sides
are 16 cm and 12 cm long,
and the perimeter of the
triangle is 36 cm ?​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given :

• Two Sides of a triangle are 16 cm and 12 cm .
• Perimeter of Triangle is 36 cm .

To Find :

• Area of Triangle

Solution :

• a = 16 cm
• b = 12 cm
• c = ?

$\longmapsto\tt{a+b+c=36}$

$\longmapsto\tt{16+12+c=36}$

$\longmapsto\tt{28+c=36}$

$\longmapsto\tt{c=36-28}$

$\longmapsto\tt\bf{c=8\:cm}$

Now ,

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{s=\dfrac{16+12+8}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{36}{2}}$

$\longmapsto\tt\bf{s=18\:cm}$

$\longmapsto\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longmapsto\tt{\sqrt{18(18-16)(18-12)(18-8)}}$

$\longmapsto\tt{\sqrt{18\:(2)\:(8)\:(10)}}$

$\longmapsto\tt{\sqrt{2\times{3}\times{3}\times{2}\times{3}\times{2}\times{5}\times{2}}}$

$\longmapsto\tt{3\times{2}\times{2}\sqrt{5\times{3}}}$

$\longmapsto\tt\bf{12\sqrt{15}\:{cm}^{2}}$

So , The Area of Triangle is 12√15 cm² ...