Question

Find the area of a traiangle two sides of which are 18cm and 10cm and the perimeter is 42cm​

Answer 1

Answer: 14 cm

Step-by-step explanation:

We know that perimeter of a triangle is the sum of three sides. So, on adding the sides 18cm and 10cm, we get 28cm. Now subtract the sum of two sides from the perimeter. We get 14cm

Answer 2

Given thαt,

• The two sides of triαngle αre 18cm αnd 10cm.
• The perimeter is 42cm.

⚫️ We need to find the αreα of the triαngle.

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Let's αssume thαt the third side be x.

$\longrightarrow{\sf{x+18+10=42}}$

$\longrightarrow{\sf{x+28=42}}$

$\longrightarrow{\sf{x=42-28}}$

$\longrightarrow{\sf{x=14}}$

Hence, the unknown side will be 14cm.

Heron's Formulα of Areα of the triαngle.

★$\large{\boxed{\sf{\orange{\sqrt{s(s-a)(s-b)(s-c)}}}}}$

Where, s = semiperimeter αnd a,b and c = sides.

★${\boxed{\sf{semiperimeter = \dfrac{a+b+c}{2}}}}$

• Substitute the values.

$\longrightarrow{\sf{\dfrac{14+18+10}{2}}}$

$\longrightarrow{\sf{\dfrac{42}{2}}}$

$\longrightarrow{\sf{21}}$

• Substitute the values in heron's formulae and simplify this.

$\implies{\sf{ \sqrt{21(21-14)(21-10)(21-18)}}}$

$\implies{\sf{ \sqrt{21(7)(11)(3)}}}$

$\implies{\sf{ \sqrt{7\times 3(7)(11)(3)}}}$

$\implies{\sf{ 7\times 3\sqrt{11}}}$

$\large{\boxed{\sf{\orange{21 \sqrt{11}}}}}$

Hence, the Areα of the triαngle is 21√11.

And we αre done! :D

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