Question

A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes ?

Answer 1

The sides of a triangle are a = 35 cm, b = 54 cm and c = 61 cm
Now, perimeter a + b + c = 25

`⇒S= 1/2(35+54+61)`

⇒s= 75cm 

By using heron’s formula

∴Area of triangle =`sqrt(s(s-a)(s-a)(s-c))`

`=sqrt(75(75-35)(75-54)(75-61))`

`sqrt(75(40)(21)(14))=93914cm^2`

∴ The altitude will be a smallest when the side corresponding to it is longest Here, longest side is 61 cm

∴ area altitude will be a smallest  when the side corresponding to is longest here' longest side is 61 cm 

∴area of Δ le = `1/2xxbxxh= 1/2xx  base xx height `

`∴1/2xxhxx61= 939.14`

`⇒= (939.14xx2)/61= 30.79 cm`

𝐻𝑒𝑛𝑐𝑒 𝑡ℎ𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑚𝑎𝑙𝑙𝑒𝑠𝑡 𝑎𝑙𝑡𝑖𝑡𝑢𝑑𝑒 𝑖𝑠 30.79 𝑐𝑚