ABC = leg x leg / 2
ABC = 6 x 8 / 2
ABC = 24
MNC = (MN / (AM+MN+NB)) x ABC
MNC = (2.5 / (1 + 2.5 + 1.5) )x 24
MNC = (1/2) x 24
MNC = 12
really hope this helps :)
Answer: Area of [tex]\triangle MNC= 12[/tex] centimeter square .
Step-by-step explanation:
According to the question, [tex]\triangle ABC[/tex] is a right angled triangle with edges AB=8 cm and AC=6 cm
And, M and N are two points in side AB Such that, AM:MN:NB=1:2.5:1.5
So, let AM=1x MN=2.5x and NB=1.5x
Since, AM+MN+NB=AB ⇒1x+2.5x+1.5x=5x
But AB=8 cm ⇒5x=8⇒x=1.6
Therefore, MN=4 cm
Now, In [tex]\triangle MNC[/tex] height= 6 cm ( shown in diagram)
while, base=4 cm
Thus, area of [tex]\triangle MNC[/tex] = 1/2×6×4=12 [tex]cm^2[/tex] ( because area of a triangle = 1/2×base×height)
