Question
Download Solution PDFComprehension
The perimeter of a triangle ABC is 105 cm. The altitudes AD, BE and CF are in the ratio 3 : 5 : 6.
What is the approximate area of the triangle ABC?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Perimeter of triangle ABC = 105 cm
Ratio of sides AB : BC : CA = 5 : 10 : 6
Formula used:
Heron's Formula for the area of a triangle:
Area =
Where a, b, c are the lengths of the sides of the triangle, and
s is the semi-perimeter s =
Calculations:
From the previous problem, we established
The ratio of the sides AB : BC : CA = 5 : 10 : 6.
Let the sides be AB = 5x, BC = 10x, and CA = 6x.
The perimeter is the sum of the sides:
Perimeter = AB + BC + CA = 5x + 10x + 6x = 21x
Given Perimeter = 105 cm.
⇒ 21x = 105
⇒ x =
⇒ x = 5
a (BC) = 10x = 10 × 5 = 50 cm
b (CA) = 6x = 6 × 5 = 30 cm
c (AB) = 5x = 5 × 5 = 25 cm
The semi-perimeter (s): s =
Area =
Area =
Area =
Area =
Area ≈ 284.975 cm2
Area ≈ 285 cm2
∴ The correct answer is option 4.
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