Question
Download Solution PDFThe area of triangle is 216 cm2 and their sides are in the ratio 3 : 4 : 5. What is the perimeter of the triangle?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Heron's formula for the area of a triangle.
\( Area=\sqrt{s(s-a)(s-b)(s-c)}\)
Here s is the semi-perimeter.
Solution:
Let the sides of the triangle be 3x, 4x, and 5x in cm.
Semi-perimeter = \(\frac{3x+4x+5x}{2}=6x\)
\( Area=\sqrt{6x(6x-3x)(6x-4x)(6x-5x)}\)
\(Area=6x^2\)
Also,
\(Area=6x^2=216\)
x = 6
Semi-perimeter = 6x = 36 cm
Perimeter = 72 cm.
Hence, option 4 is correct.
Last updated on May 26, 2025
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