If the perimeter of an isosceles right triangle is (6+3 \sqrt{2}) \m, then the area of the triangle is

Sainik School Entrance Exam 2018 Solved Paper

Question : 51 of 150

Marks: +1, -0

If the perimeter of an isosceles right triangle is

(6+3 √{2}) \m

, then the area of the triangle is

Solution:

(d)

a+a+√{2} a=6+3 √{2}

2 a+√{2} a=6+3 √{2}

a(2+√{2})=3(2+√{2})

a=3({2+√{2}}/{2+√{2}})=3

Hence, area of triangle

={1}/{2} ×b ×h

={1}/{2} × 3 ×3

={9}/{2} {\m}^2

=4.5 {\m}^2

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