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Two congruent 30-60-90 triangles are placed,as shown,so that they overlap partly and their hypotenuses coincide. If the hypotenuse is 12 cm,find the area common to the both triangles.

Respuesta :

Answer: The area common to both triangle is 31.77 sq. cm.

Step-by-step explanation:

Since we have given that

30-60-90 triangles are placed.

So, the ratio of sides would be

[tex]1:\sqrt{3}:2[/tex]

Since Hypotenuse = 12 cm

So, it becomes,

[tex]2x=12\\\\x=\dfrac{12}{2}=6[/tex]

So, Base would be

[tex]x=6\ cm[/tex]

and Perpendicular would be

[tex]\sqrt{3}x=6\sqrt{3}[/tex]

So, Area common to the both triangles would be

[tex]\dfrac{1}{2}\times base\times height\\\\=\dfrac{1}{2}\times 6\times 6\sqrt{3}\\\\=18\sqrt{3}\\\\=31.177[/tex]

Hence, the area common to both triangle is 31.77 sq. cm.

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