Question

area of a right triangle is 24 cm square and the square of the sum of the perpendicular sides 196. taking the perpendicular sides as x and y metres. a) what Number is x-y? b) what Number is x+y? c) find the lengths of sides of the right 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.

Step-by-step explanation: