Question

The altitudes of triangle are 12, 15 and 20 units. The
largest angle in the triangle is :
(A) 75°
(B) 90°
(C) 120°
(D) 135°​

Answer 1

Answer:

Let the Sides be a, b and c with Altitude 12, 15 and 20 units respectively.

• Area of Triangle :

⇒ Area = 1/2 × Base × Altitude

⇒ Area = 1/2 × a × 12

⇒ Area = 6a

⇒ Area = 1/2 × Base × Altitude

⇒ Area = 1/2 × b × 15

⇒ Area = 15b/2

⇒ Area = 1/2 × Base × Altitude

⇒ Area = 1/2 × c × 20

⇒ Area = 10c

But, 6a = 15b/2 = 10c

⇢ a/6 = 2b/15 = c/10

⇢ a/6 × 60 = 2b/15 × 60 = c/10 × 60

⇢ 10a = 8b = 6c

⇢ 5a = 4b = 3c

⇢ a : b : c = 5 : 4 : 3

we can see that the Sides are in Ratio 3,4 and 5 that is Pythagorean Triplet.

So Triangle would must be Right Angle.

Hence, Largest Angle is B) 90°