Question

In a right-angled triangle, one of the perpendicular sides is 6 centimeter longer than the other side. If the area of the triangle is 36 square centimeter, Find the lengths 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

⇒1/2×a×(a+6)=36

⇒a²+6a=72

⇒a²+6a−72=0

⇒a²+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.