Question

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.

Answer 1

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

$1:\sqrt{3}:2$

Since Hypotenuse = 12 cm

So, it becomes,

$2x=12\\\\x=\dfrac{12}{2}=6$

So, Base would be

$x=6\ cm$

and Perpendicular would be

$\sqrt{3}x=6\sqrt{3}$

So, Area common to the both triangles would be

$\dfrac{1}{2}\times base\times height\\\\=\dfrac{1}{2}\times 6\times 6\sqrt{3}\\\\=18\sqrt{3}\\\\=31.177$

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