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  • The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 24 m. Then the area of the triangle is (in m2) Option: 1</

The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 24 m. Then the area of the triangle is (in m2) 

Option: 1

16


Option: 2

24


Option: 3

28


Option: 4

20


Answers (1)

Let the lengths of the sides be a, b and c respectively.

So, a = 3x, b = 4x and c = 5x

3x+4x+5x = 24m

12x = 24m

x = 2m

we get a = 6 m, b = 8 m and c = 10 m

s = \frac{a+b+c}{2} = 12

s - a = (12 - 6)m = 6m

s - b = (12 - 8)m = 4m

s - c = (12 -10)m = 2m

Area\hspace{0.2cm} of \hspace{0.2cm}a\hspace{0.2cm} triangle =\sqrt{s(s-a)(s-b)(s-c)}

=\sqrt{12\times 6\times 4\times 2}\;m^2=24m^2 

Posted by

Kshitij

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