Let a,b,c be lengths of the sides of a right angled triangle where c is the length of the hypotenuse. Given that a=15 and c+b=25, find the value of c.

Sure, let's solve this step by step:

Step 1: We know that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). This is known as the Pythagorean theorem. So, we have:

c² = a² + b²

Step 2: We are given that a = 15. So, we can substitute this into our equation:

c² = 15² + b² c² = 225 + b²

Step 3: We are also given that c + b = 25. We can rearrange this equation to find b:

b = 25 - c

Step 4: Now, we can substitute b = 25 - c into our equation from step 2:

c² = 225 + (25 - c)²

Step 5: Simplify the equation:

c² = 225 + 625 - 50c + c² 0 = 850 - 50c 50c = 850 c = 850 / 50 c = 17

So, the length of the hypotenuse (c) is 17 units.