heya!!

Here is your answer -

Let the length of one perpendicular be a cm.

Then, the length of the other perpendicular =(a+6)cm

Now, area of triangle =36 sq.cm

⇒  1/2​×a×(a+6)=36

⇒a^2 +6a=72

⇒a^2 +6a−72=0

⇒a^2+12a−6a−72=0

⇒(a+12)(a−6)=0

⇒a=12 or a=6

But length cannot be negative, hence a=6 cm

Thus length of its perpendicular sides are, a=6 cm and a+6=12 cm.

Answer:

Let the length of one perpendicular be a cm.

Then, the length of the other perpendicular =(a+6)cm

Now, area of triangle =36 sq.cm

⇒

2

1

×a×(a+6)=36

⇒a

2

+6a=72

⇒a

2

+6a−72=0

⇒a

2

+12a−6a−72=0

⇒(a+12)(a−6)=0

⇒a=12 or a=6

But length cannot be negative, hence a=6 cm

Thus length of its perpendicular sides are, a=6 cm and a+6=12 cm.