Question

in a right angled triangle one of the perpendicular sides is6cm longer than the other side.If the area of the triangle is 36cm² find the length of its perpendicular sides​

Answer 1

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