Question

the difference in the sides along the right angle in a right traingle is 14 cm if the area of triangle is 120 c. find the perimeter of the triangle​

Answer 1

Answer:

Let the sides at right angles in the given right-angled triangle be a and b.

Without loss of generality, we let a>b.

The by the problem a−b=14⇒a=(b+14)........(1).

Now the are of the right-angled triangle be

2

1

×a×b=

2

b(b+14)

cm

2

. [Using (1)]

According to the problem

2

b(b+14)

=120

b

2

+14b−240=0

(b−10)(b+24)=0

This gives b=10⇒a=24.

Now the hypotenuse of the right-angled triangle be

10

2

+24

2

=26 cm.

Now the perimeter of the triangle be (10+24+26)=60 cm.