The area of a triangle is 54 cm2and its sides are in the ratio 3: 4 :

1.	The area of a triangle is 54 cm2and its sides are in the ratio 3: 4 : 5. What is its perimeter?with proper explanation
Answer» 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.

The area of a triangle is 54 cm2and its sides are in the ratio 3: 4 : 5. What is its perimeter?with proper explanation

Answer»

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}

+12

81+144

225

=>15cm

So perimeter

= 9+12+15

=36 cm

hope it MAY help you.