Question

The area of a triangle is 54 cm

2

and its sides are in the ratio 3: 4 : 5. What is its

perimeter?with proper explanation​

Answer 1

Answer:

36 cm

Here given ;

Area =54cm^2

and the difference between two sides of right angles triangle is 3cm.

So, let the sides be x and x+3

Area = 54

=>1/2(x)(x+3)=54

=>(x^2+3x)/2=54

=>x^2+3x=108

=>x^2+3x-108=0

=>(x+12)(x-9)=0

we get x= -12 and 9

we can't take negative ,so

x=9cm

and other side is x+3=12 cm

now ,hypotenuse

=

\begin{gathered} \sqrt{ {9}^{2} + {12}^{2} } \\ = > \sqrt{81 + 144} \\ = > \sqrt{225} \\ = > 15cm\end{gathered}

9

2

+12

2

=>

81+144

=>

225

=>15cm

So perimeter

= 9+12+15

=36 cm

hope it may help you.

Answer 2

Answer:

since its side is in ratio 3:4:5 it is right triangle

3^2+4^2=9+16=25=5^2

let us suppose that it's base and height be 3x and 4x

1/2*4x*3x=54

x^2=54*2/12

x^2=9

x=3

sides of triangle 9,12,15

perimeter=9+12+15=36cm