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In the following question, 3 statements are given. You have to find which is/are necessary and sufficient to answer the following question.  Find the area of the Triangle ABC Statement I∶ Perimeter of the triangle is 100. Statement II∶ Sum of the largest and smallest side of the triangle is 73. Statement III∶ The triangle is an isosceles triangle.

In the following question, 3 statements are given. You have to find which is/are necessary and sufficient to answer the following question.  Find the area of the Triangle ABC Statement I∶ Perimeter of the triangle is 100. Statement II∶ Sum of the largest and smallest side of the triangle is 73. Statement III∶ The triangle is an isosceles triangle. Correct Answer statement I, statement II and statement III are sufficient

Statement I

AB + AC + BC = 100

Statement II

Let the largest triangle side is BC and smallest is AB

AB + BC = 73

Statement III

Isosceles triangle

AB = AC

⇒ 2AB + BC = 100

⇒ AB = 100 – 73

⇒ AB = 27

AB = 27, AC = 27, BC = 46

We have all the side now we can calculate the area of the triangle

∴ statement I, statement II and statement III are sufficient

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