Question

If the sides of a triangle are 17cm, 25cm and 26cm, then its area is *

204 sq.cm

240 sq.cm

200 sq.cm

34 sq.cm


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Answer 1

Step-by-step explanation:

a is the correct answer

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Answer 2

● Given :-

• Sides of triangle.
• Let side a, b, c
• a = 17 cm
• b = 25 cm
• c = 26 cm

● To find :-

• Area of triangle.

● Solution :-

Let s be the semiperimeter of triangle.

》So, Semiperimeter is :-

$\sf{ \longmapsto{ \dfrac{a + b + c}{2} }} \\ \\ \sf{ \longmapsto{ \dfrac{17 + 25 + 26}{2} }} \\ \\ \sf{ \longmapsto{ \dfrac{68}{2} }} \\ \\ { \boxed{ \blue{ \longmapsto{ \sf{34 \: cm}}}}}$

》Now area of triangle is :-

By Heron's formula:

$\sf{ \longmapsto{ \sqrt{s(s - a)(s - b)(s - c)} }} \\ \\ \sf{ \longmapsto{ \sqrt{34(34 - 17)(34- 25)(34 - 26)} }} \\ \\\sf{ \longmapsto{ \sqrt{34 (17)(9)(8)} }} \\ \\ \sf{ \longmapsto{ \sqrt{17 \times 2 \times 17 \times 3 \times 3 \times 2 \times 2 \times 2} }} \\ \\ \sf{ \longmapsto{ 17 \times 2 \times 2 \times 3 }} \\ \\ \large{ \underline{ \boxed{ \red{\sf{ \longmapsto{Area \: =204 \: {cm}^{2} }} }}}}$

So, option 1 is correct.