Find the sum please fast a bit faster

Dear student

​​​Let the base of triangle be b cm and its height or perpendicular be p cm.
 


Given difference between two sides of right angles triangle is 2 cm

 p - b = 2  ... (1)

and area of triangle = 24 cm2
 

On putting the value of b in (1), we get
p-48p=2p2-48p=2p2-48=2p

p2 - 2p -48 = 0

p2 - 8p + 6p -48 = 0

  p(p-8)+6(p-8)=0

⇒ (p- 8) (p + 6) = 0

p = 8, -6

p ≠ -6. So, p = 8 cm (length can't be negative)

On putting p in (1), we get

b = 6 cm

So, Hypotenuse (h) =

Hence, perimeter of triangle = p + b + h = 8 cm + 6 cm + 10 cm = 24 cm

Regards

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