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
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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
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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.
Verified answer
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