Question

Area of a right angled triangle is 216 square cm.One of the perpendicular sides is 6 more than the

other.

a) If the smallest side is x then what is the side perpendicular to it?

b) Form a second degree equation connecting perpendicular sides and area .

c) Find the perpendicular sides of the triangle.

d) Find the hypotenuse of the triangle.​

Answer 1

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.