Question

the sides of a triangle are 8cm, 15cm, 17cm find its area​

Answer 1

It is a right angled triangle

Because

$17 {}^{2} = 15 {}^{2} + 8 {}^{2} \\ 289 = 225 + 64 \\ 289 = 289$

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Answer 2

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

Area of the ∆ is 60cm².

${\blue{\underline{\underline{\purple{\textsf{\textbf{ Explanation : }}}}}}}$

Given that,

➡Three sides of a ∆ are : 8cm, 15cm, and 17cm.

Using the Heron's formula :

${ \pink {\sf{ \longrightarrow \: area \: of \: a \: \triangle \: = \sqrt{s(s - a)(s - b)(s - c)} }}}$

Here,

a = 8cm.

b = 15cm.

c = 17cm.

s (semi-perimeter) = ?

• Here we need to find the semi perimeter (s) to apply on herons formula.

As we know that,

➪ Semi perimeter = ½ × (a + b + c)

➡ ½ × (8+15+17)

➡ ½ × (40)

➡ 20cm.

Therefore, semi-perimeter is 20cm.

❐ Procedure :

• Here, we'll represent ‘‘area of the ∆’’ as ‘a’

$\sf \longrightarrow a = \sqrt{20(20 - 8)(20 - 15)(20 - 17)}$

$\sf \longrightarrow a = \sqrt{20(12)(5)(3)}$

$\sf \longrightarrow a = \sqrt{20(180)}$

$\sf \longrightarrow a = \sqrt{3600}$

$\sf \longrightarrow a = 60cm.$

${{\underline{\underline{{\textsf{\textbf{Hence : }}}}}}}$

➪ Area of the ∆ is 60cm²

Note behind :

• To solve this question we've used the herons formula of where we're needed to find the semi-perimeter and then assuming ‘a’ as the ‘area of ∆’ we have got our final answer.