Question

The side of right triangle ABC are 5 cm,12cm,13cm.find the area of the triangle

Answer 1

$\sf\huge\blue{\underline{\underline{ Question : }}}$

The side of right triangle ABC are 5 cm,12cm,13cm.find the area of the triangle.

$\sf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

◼ Sides of triangle = 5cm, 12cm, 13cm.

★ To find,

◼ Area of triangle.

★ Formula used :

Heron's Formula :

$\tt\red{:\implies \sqrt{S(S - a)(S - b)(S - c)}}$

Where,

$\tt\red{ :\implies S = \frac{a + b + c}{2}}$

★ Let,

• a = 5
• b = 12
• c = 13

$\bf\:\leadsto S = \frac{5 + 12 + 13}{2}$

$\bf\:\leadsto S = \frac{30}{2}$

$\bf\:\leadsto S = 15$

$\boxed{\therefore Hence,\:S = 15}$

★ Now,

$\bf\:\leadsto \sqrt{15(15 - 5)(15 - 12)(15 - 13)}$

$\bf\:\leadsto \sqrt{15(10)(3)(2)}$

$\bf\:\leadsto \sqrt{900}$

$\bf\:\leadsto 30$

$\underline{\boxed{\rm{\purple{\therefore Area\:of\:triangle= 30\:cm^{2}.}}}}\:\orange{\bigstar}$

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Answer 2

Aɴsᴡᴇʀ :

➛ The area of the traingle = 30 cm²

Gɪᴠᴇɴ :

• Sides of right angle traingle = 5 cm, 12cm, 13cm

Tᴏ Fɪɴᴅ :

• The area of the traingle = ?

Sᴏʟᴜᴛɪᴏɴ :

The three sides of the traingle are

⪼ a = 5

⪼ b = 12

⪼ c = 13

Semi perimeter (s) $= \sf{\dfrac{a + b + c}{2}}$

Semi perimeter (s) $=\sf{\dfrac{5 + 12 + 13}{2}}$

Semi perimeter (s) $=\sf{\dfrac{\cancel{30}}{\cancel{\:2\:}}}$

Semi perimeter (s) = 15

Now,

By heron's formula

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

$\sf{:\implies \sqrt{15(15 - 5)(15 - 12)(15 - 3)} }$

$\sf{: \implies \sqrt{15 \times 10 \times 3 \times 2} }$

$\sf{: \implies \sqrt{900} }$

$\sf{: \implies \underline{ \overline{ \boxed{ \purple{ \bf{ \: \: 30 \: cm^2\: \:}}}}}}$

Hence, the area of the traingle is 30 cm².