Question

ne ratio of sides of a triangle is 3:4:5 and area of the triangle is 72 square units. Then the area of an equilateral triangle whose perimeter is same as that of the previous triangle is SSC CGL (Tier-II) 2012 (1) 32 73 square units (2) 48 73 square units (3) 96 square units (4) 60/3 square units

11th - 12th Class

Maths

Solution

119

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Sol. (2) Let the sides of triangle are ( 3 x, 4 x ) and ( 5 x ) units Here, ( (3 x)^{2}+(4 x)^{2}=(5 x)^{2} ) ( therefore ) It is a right angled triangle. Now, Area of triangle ( =frac{1}{2} times 3 x times 4 x=6 x^{2} ) ( therefore 6 x^{2}=72 ) ( Rightarrow x^{2}=frac{72}{6} ) ( Rightarrow x=sqrt{12}=2 sqrt{3} ) Perimeter of right angled triangle ( =3 x+4 x+5 x ) ( =12 x=12 times 2 sqrt{3} ) ( =24 sqrt{3} ) units ( therefore ) Perimeter of equilateral triangle ( =24 sqrt{3} ) units Its side ( =frac{24 sqrt{3}}{3}=8 sqrt{3} ) units Area ( =frac{sqrt{3}}{4} times(text { side })^{2} ) ( =frac{sqrt{3}}{4} times 8 sqrt{3} times 8 sqrt{3} ) ( =48 sqrt{3} ) sq units.