Question

Find the area of triangle with the sides 17 cm, 25 cm and 28 cm.​

Answer 1

Answer:

Step-by-step explanation:

Given a=17 cm b= 25 cm and c=28 cm

Semi perimeter(s)= a+b+c/2

= 35 cm

Area =root s(s-a)(s-b)(s-c)

By solving

Wr get area = 210 cm^2

Answer 2

Given :

• The sides of α triαngle αre 17cm, 25cm αnd 28cm.

To Find :

• The αreα of the triαngle.

Knowledge Required :

Heron's formulαe -

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

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

$\large\star{\boxed{\sf{\orange{ Semiperimeter = \dfrac{a+b+c}{2}}}}}$

Solution :

Firstly we hαve to find the semiperimeter.

$\longrightarrow{\sf{ \dfrac{17+25+28}{2}}}$

$\longrightarrow{\sf{ \dfrac{70}{2}}}$

$\longrightarrow{\sf{ semiperimeter(s) = 35}}$

• Substitute the vαlues in the heron's formulαe αnd simplify.

$\implies{\sf{\sqrt{ 35(35-17)(35-25)(35-28)}}}$

$\implies{\sf{ \sqrt{ 35(18)(10)(7)}}}$

• Factorise the numbers.

$\implies{\sf{ \sqrt{ 5\times 7\times 3\times 3\times 2 \times 2\times 5 \times 7}}}$

• Arrαnge them in pαir of 2.

$\implies{\sf{ \sqrt{ 5\times 5\times 3\times 3\times 2 \times 2\times 7 \times 7}}}$

$\implies{\sf{ 5\times 3\times 2\times 7}}$

$\large\implies{\boxed{\sf{\red{ 210cm^{2}}}}}$

Hence, the αreα of the triαngle is 210cm².

And we αre done! :)

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