Question

If the area of a triangle is 54cm square and the difference between the sides of a right angles triangle is 3cm, find its perimeter​

Answer 1

Answer:

Given, difference between the sides of a right any led triangle = 3 cm and area of right angled triangle = 54 cm2

Let p, b, h be the perpendicular, base and hypotenuse of given right angled triangle respectively.

∴ Difference between the sides of triangle = Base – perpendicular of triangle

⇒ b – p = 3

⇒ b = 3 + p ... (1)

Again, Area of right angled triangle = 54

p ≠ –12, because perpendicular of a triangle cannot be negative

∴ p = 9

On putting value of p in (1) we get

b = 3 + p

⇒ b = 3 + 9 = 12 cm

Now, the hypotenuse of right angled triangle

∴ Perimeter of triangle = Sum of its all sides

= h + p + b

= 15 + 9 + 12 = 36 cm

Hence, the perimeter of given right angle triangle is 36 cm.

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Answer 2

Answer:

36 cm

Step-by-step explanation:

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

=

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

So perimeter

= 9+12+15

=36 cm

hope this helps☺️☺️