A square and an equilateral triangle have equal sides. If the square

Question

A square and an equilateral triangle have equal sides. If the square has diagonal  10\sqrt{2} , what is the area of the triangle?

A.  50\sqrt{3}

B.  50\sqrt{2}

C. 50

D.  25\sqrt{3}

E. 25

pushpitkc · Answer

Diagram.png Formula used: Area of equilateral triangle = \frac{\sqrt{3}}{4} * a^2 where a - side of equilateral triangle Diagonal of square = c\sqrt{2} | Area of the square = c^2 where c - side of the square Given: Diagonal = 10\sqrt{2} . From this we deduce the side of square is 10 One side of the equilateral triangle, which coincides with one of the sides of the triangle, is equal to 10 Therefore, the area of an equilateral triangle is \frac{\sqrt{3}}{4} * 10^2 = 25\sqrt{3} (Option D)

Sreyoshi007 · Answer

The diagonal of a square is given by  a\sqrt{2} 
 
Since diagonal is given to be  10\sqrt{2} , 
 a\sqrt{2}  =  10\sqrt{2} ,

a = 10

Area of an equilateral triangle is (  \sqrt{3}  /4)* a^2.
since a = 10,
 ((  \sqrt{3}  )/4)* 10^2.
(100/4) *  \sqrt{3} 
-> 25 \sqrt{3}

Hence answer is  option D .

Abhishek009 · Answer

a\sqrt{2} = 10\sqrt{2}

So,  a = 10 = s

Area of an Equilateral Triangle =  s^2\sqrt{3}/4

Or, Area of an Equilateral Triangle =  100\sqrt{3}/4

Or, Area of an Equilateral Triangle =  25\sqrt{3} , Answer must be (D)

A square and an equilateral triangle have equal sides. If the square

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A square and an equilateral triangle have equal sides. If the square

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