Question

in a right triangle ABC M is the midpoint of AC and MN perpendicular to BC. If AC =20 cm BC 16 cm

a) find the length of AB
b)find tge area of ABC AND MNC​

Answer 1

Step-by-step explanation:

AC^2=AB^2+BC^2

20^2=AB^2+16^2

400-256=AB^2

AB^2=144

AB=12

A(∆ABC)=1/2×BC×AB

=1/2×16×12

=8×12

=96cm^2

MC=1/2×AC

=10cm

∆ABC , is a scalene triangle

because all sides are different.

so, angle B=N=90°

angle A=M=30°

angle C=C=60

so, by 30,60,90 theorem

Seg NC is opposite of 30°

NC=1/2×MC

=1/2×10

NC =5

Seg MN is opposite of 60°

MN=√3/2×NC

=√3/2×5

=2.5√3cm

height=MN

Base=NC

A(∆MNC)=1/2×NC×MN

=1/2×5×2.5√3

=2.5×2.5√3

=6.25√3cm^2