Two sides of a triangle forming a right angle are 6x² and (2x²-1). If the area of the triangle is 84 square units, then what is the perimeter of the triangle?
A.59 units
B.53 units
C.51 units
D.56 units✓ Correct
Explanation
Area = (1/2)·6x²·(2x²-1) = 84, so 3x²(2x²-1)=84, 6x⁴-3x²-84=0, 2x⁴-x²-28=0. Let y=x²: 2y²-y-28=0, y=(1+√225)/4=4, x²=4, x=2. Sides: 24, 7, hypotenuse=25. Perimeter=56.
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