Question

The diagonal of a square is equal to the side of an equilateral triangle. If the area of the square is 153 sq cm, what is the area of the equilateral triangle?

Answer 1

Answer:132.49 sq. cm

Step-by-step explanation:

Answer 2

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Answer:

Area of the square = a² = 153 sq cm                                                                  => a = √153 = 12.369 cm

Now ,the square forms a right angled triangle with 2 sides equal to 'a' . And another side will be the hypotenuse ,let it's length be 'l'.

Now we have to use the formula PYTHAGORAS THEOREM to find the length of hypotenuse or diagonal of the square.

=> a² + a² = l²

Step-by-step explanation:

=> 2a² = l²

=> 2* [12.369]² = l²

=> 2 * 153 = l²

=> 306 = l²

=> l = 17.492 cm

Here 'l' is the diagonal of the square or the side of an equilateral triangle.

So, Area of an equilateral triangle ,A= √3l²/4

=> A = √3 * 306/2

=> A = 153√3

=> A = 265 sq. cm

Hence area of the required equilateral triangle is 265 sq. cm.

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