Question

The sides of a triangle measure 17cm 25cm 26cm.find the length of the altitude corresponding to the sortest side.

Answer 1

Hey!

Given,
a = 17 cm, b = 25 cm, c = 26 cm

We know,
s = a+b+c/2
s = 17+25+26/2
s = 68/2
s = 34

Now,
Area = √s(s-a)(s-b)(s-c)
         = √34(34-17)(34-25)(34-26)
         = √34 x 17 x 9 x 8
         = √2 x 17 x 17 x 3 x 3 x 2 x 2 x 2
         = 2 x 2 x 17 x 3
         = 204 cm^2

Now, Length of altitude corresponding to largest side---
 
area = 1/2 base x altitude
area = 1/2 x 17 x AM
204 = 1/2 x 17 x AM
204 x 2/17 = AM
24 = AM
or
AM = 24

Hence, the length of altitude corresponding to shortest side = 24 cm

Answer 2

Step-by-step explanation:

you can see the attachment