Question

Maximum number of equilateral triangles with side 3 cm that can be fitted in a large equilateral triangle of side 11.2 cm

Answer 1

to solve this problem first find area of large equilitral triangle then find area of small triangle and thenbdivide area of larg e by small traingle

Answer 2

Answer:

1

Step-by-step explanation:

Side of large equilateral triangle = 11.2cm

To calculate the area of given triangle we will use the heron's formula :

$Area = \sqrt{s(s-a)(s-b)(s-c)}$

Where $s = \frac{a+b+c}{2}$

a,b,c are the side lengths of triangle  

a =11.2 cm

b =11.2 cm

c =11.2 cm

Now substitute the values :

$s = \frac{11.2+11.2+11.2}{2}$

$s =16.8$

$Area = \sqrt{16.8(16.8-11.2 )(16.8-11.2 )(16.8-11.2 )}$

$Area =54.3171133254$

Thus the area of the large triangle is 54.3171133254 square cm.

Side of small triangle = 3 cm

To calculate the area of given triangle we will use the heron's formula :

$Area = \sqrt{s(s-a)(s-b)(s-c)}$

Where $s = \frac{a+b+c}{2}$

a,b,c are the side lengths of triangle  

a =3 cm

b =3 cm

c =3cm

Now substitute the values :

$s = \frac{3+3+13}{2}$

$s =9.5$

$Area = \sqrt{9.5(9.5-3 )(9.5-3 )(9.5-3 )}$

$Area =51.0777593479$

Thus area of small equilateral triangle is 51.0777593479 sq.cm.

Maximum number of equilateral triangles with side 3 cm that can be fitted in a large equilateral triangle of side 11.2 cm = $\frac{54.3171133254}{51.0777593479}=1.063$

So, 1 equilateral triangle of side 3 cm can be fitted in a large equilateral triangle of side 11.2 cm.