SOLUTION: A triangle with sides of 32cm, 60cm and 68cm is cut into parts that form a quadrilateral. Find, in cm2, the area of the largest quadrilateral that can be formed.

Algebra ->  Triangles -> SOLUTION: A triangle with sides of 32cm, 60cm and 68cm is cut into parts that form a quadrilateral. Find, in cm2, the area of the largest quadrilateral that can be formed.      Log On


   

Question 1148866: A triangle with sides of 32cm, 60cm and 68cm is cut into parts that form a quadrilateral. Find, in cm2, the area of the largest quadrilateral that can be formed.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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Notice that  32%5E2 + 60%5E2 = 4624 = 68%5E2,


so the triangle is a right angled triangle.


Hence, its area is half of the product of the lengths of its legs


    area = %281%2F2%29%2A32%2A60 = 960   = 16*60 = 16*4*15 = 4%5E3%2A15 = 2%5E6%2A15.


Then the side length of the square is  sqrt%28960%29 = sqrt%282%5E6%2A15%29 =2%5E3%2Asqrt%2815%29 = 8%2Asqrt%2815%29 = 30.984 cm^2  (approximately).    ANSWER

Solved.