Let AB = 24 cm
BC = 7cm Using Pythagoras theorem, we have
AC² = AB² + BC²
= (24 cm)²+ (7 cm)²
= 576 cm² + 49 cm²
= 625 cm²
So, AC = 25 cm

Now,

Let
PQ = 12K
and
PR = 13K
Using Pythagoras theorem, we have
PR² = PQ² + QR²
⇒(13K)² = (12K)² + QR²
⇒169K² = 144K² + QR²
⇒QR² = 169K² - 144K²
⇒QR² = 25K²
So, QR = 5K

Now, 

Therefore,

Let us draw a right angle triangle, right angled at B.
We know that:

 Let BC = 3K,  AC = 4K
where K is a positive number.

Using Pythagoras theorem, we have
                 
        
              
              
               
               
Now,  
and    

Let us draw a right triangle ABC, right angled at B.
It is given that:
15 cot A = 8
              

Let
AB = 8K, BC = 15K
Using Pythagoras theorem, we have
AC² = AB² + BC² = (8K)² + (15K)²
= 64K² + 225K²
= 289K²
So,
AC = 17K
Now,
AC = 17K