Question

Find the altitude of a triangle which lie on the
smaller side of the triangle, whose side is 14
cm, 16 cm, and 18 cm respectively.​

Answer 1

Answer: Given, sides of triangle 5 cm, 12 cm, 13 cm.

Now semi perimeter, s= =  

2

sum of the sides of triangle

​  

 

=  

2

5+12+13

​  

=15 cm

Using heron's formula, Area of triangle=  

s(s−a)(s−b)(s−c)

​  

 

=  

15(15−5)(15−12)(15−13)

​  

 

=  

15×10×3×2

​  

=30cm  

2

 

Using altitude, area of triangle =  

2

1

​  

× base × altitude =30cm  

2

 

=  

2

1

​  

×13× altitude =30

= altitude =  

13

30×2

​  

=4.61 cm

So, altitude corresponding to largest side is 4.61 cm.

Step-by-step explanation:

Answer 2

Answer:

Given, sides of triangle 5 cm, 12 cm, 13 cm.

Now semi perimeter, s= =

2

sum of the sides of triangle

=

2

5+12+13

=15 cm

Using heron's formula, Area of triangle=

s(s−a)(s−b)(s−c)

=

15(15−5)(15−12)(15−13)

=

15×10×3×2

=30cm

2

Using altitude, area of triangle =

2

1

× base × altitude =30cm

2

=

2

1

×13× altitude =30

= altitude =

13

30×2

=4.61 cm

So, altitude corresponding to largest side is 4.61 cm.