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# A Triangle Has Sides 35 Cm, 54 Cm and 61 Cm Long. Find Its Area. Also, Find the Smallest of Its Altitudes ? - CBSE Class 9 - Mathematics

ConceptArea of a Triangle by Heron’S Formula

#### Question

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

#### Solution

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

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#### APPEARS IN

Solution A Triangle Has Sides 35 Cm, 54 Cm and 61 Cm Long. Find Its Area. Also, Find the Smallest of Its Altitudes ? Concept: Area of a Triangle by Heron’S Formula.
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