Question

In ΔABC, AB=17, BC=15, AC=8, find the length of the median on the largest side.

Answer 1

It is given that ,

In ∆ABC ,

AB = c = 17 ,

BC = a = 15

AC = b = 8

CD = m is a median of largest side AB .

m² = ( 2a² + 2b² - c² )/4

= [ ( 2 × 15² + 2 × 8² - 17² ) ]/4

= ( 578 - 289 )/4

= 289/4

m = √ ( 289/4 )

m = 17/2

m = 8.5

Therefore ,

median = CD = m = 8.5

I hope this helps you.

: )

Answer 2

Dear Student,

Answer: CD = 8.5 cm

Solution:

For all the dimensions please see the diagram attached .

Now let us assume that length of longest side median be l.

It is given by

Parallelogram law

2b² +2a² = c² +(2l)²

l² =( 2a² + 2b² -c²)/4

here a = 8 cm

b = 15 cm

c = 17 cm

l² =( 2(8)²+2(15)² -(17)²)/4

l² = (128+450-289)/4

l² = 72.25

l = √ 72.25

l = 8.5 cm

So, length of median be CD = 8.5 cm

Hope it helps you.