Question

On the (Be's right angle, Des the midpoint of the Side
tc. if AB=6cm, Ber8cm, then the
length
of BD is​

Answer 1

Answer:

BD=6.2 cm

Step-by-step explanation:

In triangle ABC

Angle B=90 degree

AB=6 cm

BC=8 cm

D is the mid-point of AC.

In triangle ABC

AC^2=AB^2+BC^2AC

2

=AB

2

+BC

2

Using Pythagoras theorem

(hypotenuse)^2=(Base)^2+(perpendicular\;side)^2(hypotenuse)

2

=(Base)

2

+(perpendicularside)

2

AC^2=6^2+8^2AC

2

=6

2

+8

2

AC^2=36+64AC

2

=36+64

AC^2=100AC

2

=100

AC=\sqrt{100}=10 cmAC=

100

=10cm

AD=DC=\frac{1}{2}AC=\frac{1}{2}(10)=5 cm

2

1

AC=

2

1

(10)=5cm

We know that when a line is drawn from vertex and divide the opposite side into equal parts then, it will be perpendicular .

In right triangle DBC

BC^2=DB^2+DC^2BC

2

=DB

2

+DC

2

Substitute the values

8^2=DB^2+5^28

2

=DB

2

+5

2

64=DB^2+2564=DB

2

+25

DB^2=64-25=39DB

2

=64−25=39

DB=\sqrt{39}=6.2 cmDB=

39

=6.2cm