Question

the sides of a triangle are 35cm, 54cm, 61cm , respectively. the length of its longest altitude

Answer 1

calculate the area by Heron's formula 
Area=1211 sq. cm.  (approx.)

Put it equal to the formula1/2*base*height  
where base=smallest side=35cm 
doing this you get the required altitude=69.20cm  (approx.)

Answer 2

Answer:

The length of its longest altitude is 53.665 cm

Step-by-step explanation:

Sides of triangle :

a = 35 cm

b = 54 cm

c = 61 cm

We will use Heron's formula to find the area of triangle

$Area = \sqrt{s(s-a)(s-b)(s-c)}$

where $s =\frac{a+b+c}{2}$

Substitute the values :

$s =\frac{35+54+61}{2}$

$s =75$

$Area = \sqrt{75(75-35)(75-54)(75-61)}$

$Area = 939.1485 cm^2$

now we are supposed to find the length of its longest altitude

Smallest side = 35 cm

So, area of triangle = $\frac{1}{2} \times Base \times height$

$939.1485 =\frac{1}{2} \times 35  \times height$

$\frac{939.1485 \times 2}{35} =height$

$53.665=height$

Hence The length of its longest altitude is 53.665 cm