In the right triangle △ABC, leg AC=6 cm and leg BC=8 cm. Point M and N belong to AB so that AM:MN:NB=1:2.5:1.5. Find area of △MNC.

Question

In the right triangle △ABC, leg AC=6 cm and leg BC=8 cm. Point M and N belong to AB so that AM:MN:NB=1:2.5:1.5. Find area of △MNC.

0

Answers ( No )

    0
    2021-09-10T20:21:03+00:00

    Answer:  Area of \triangle MNC= 12 centimeter square .

    Step-by-step explanation:

    According to the question, \triangle ABC 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 \triangle MNC height= 6 cm ( shown in diagram)

    while, base=4 cm

    Thus, area of  \triangle MNC = 1/2×6×4=12 cm^2   ( because area of a triangle = 1/2×base×height)

    0
    2021-09-10T20:21:08+00:00

    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 🙂

Leave an answer

Browse
Browse