Question

the difference between sides at right angles ina right angled triangle is 14cm .the area of the triangle is 120cm square .the perimeter of the triangle is​

Answer 1

Answer:

the difference between sides at right angles ina right angled triangle is 14cm .the area of the triangle is 120cm square .the perimeter of the triangle is

Answer 2

Answer:

Step-by-step explanation:

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.