Question

The sides of a triangle are 11 cm, 15 cm and 16 cm. The altitude to the largest side is
A. 30 √7 cm
B. 15√7/2 cm
C. 15√7/4 cm
D. 30 cm

Answer 1

Answer:

C. 15root7/2 cm is correct answer.

Answer 2

Given : The sides of a triangle are 11 cm, 15 cm and 16 cm.

 

Let the length of the sides of the triangle are a = 11 cm, b = 15 cm and c = 16 cm.

 

Semi perimeter of Δ (s) = (a + b + c)/2

s = (11 + 15 + 16)/2

s = 42/2  

s = 21 cm

By using Heron's formula :  

 Area of ∆ , A = s√(s - a)(s - b)(s - c)  

A = √21(21 - 11) (21 - 15) (21 - 16)

A = √21 × 10 × 6 × 5

A = √(7 × 3) ×  (5 × 2) ×  (2 × 3) (5)  

A = √(3 × 3) × (2 × 2) × (5 × 5) ×  7  

A = 3 × 2 × 5 ×√7  

Area of ∆, A = 30√7 cm²

Altitude to the largest side :

Area of ∆ = ½ × base × altitude  

30√7 = ½ × 16 × altitude

30√7 = 8 × altitude

Altitude = 30√7/8

Altitude = 15√7/4 cm  

Hence, Altitude to the largest side 15√7/4 cm .

Option (C) 15√7/4 is correct.

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