how many Triangles can make in 24 centimetre square
Answers
Answer:
Let a=8 cm , b =6 cm and angle between
sides a and b is C. Area of triangle ABC =
1/2.a.b.sinC.
1/2.8 cm.6 cm.sinC = 12 cm^2
24 cm^2.sinC=12 cm^2
sinC= 12cm^2/24 cm^2= 1/2
C= 30° ,150° are only possible (as sum of all
interior angles is 180°).
Thus, only two triangles are possible in which
in 1st triangle angle between given sides is 30°
and in 2nd triangle angle between sides is
150°. , Answer.
Second method:-
Let third side is x cm long.
a= 8 cm , b = 6 cm and c = x cm.
s=(a+b+c)/2=(8+6+x)/2= 7+(x/2).
Area of triangle =[s (s-a) (s-b) (s-c)]^1/2
12 =[{7+(x/2)}.{x/2–1}.{x/2+1}.{7-x/2}]^1/2
12 =[{49-x^2/4}.{x^2/4–1}]^1/2
On squaring both sides
144 =49x^2/4–49-x^4/16+x^/4
193 =50x^2/4-x^4/16
x^4/16–50x^2/4+193 =0
(x^2/4)^2–2×(x^2/4)×25+(25)^2–625+193=0
(x^2/4 -25)^2= 432.
(x^2/4-25)= +/-12.(3^1/2) = +/-20.784
x^2/4 = 25 +/-20.784
x^2/4= 45.784 , 4.216
x^2= 183.136 , 16.864
x= 13.53 cm , 4.11 cm.
Hare both the length of 3rd side are possible
to construct the triangle, so that two triangles
are possible. , Answer.
to make a square we need 2 triangles....