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=133 and c+b=361, 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 = 133. So, we can substitute this into our equation:

c² = (133)² + b²

Step 3: We are also given that c + b = 361. We can rearrange this equation to find b in terms of c:

b = 361 - c

Step 4: Now, we can substitute b = 361 - c into our equation from step 2:

c² = (133)² + (361 - c)²

Step 5: Now, we can solve this equation for c. This is a quadratic equation, and we can solve it by factoring, completing the square, or using the quadratic formula.

After solving, we get two possible values for c, 361 and 228. But since c is the hypotenuse and must be the longest side, c = 361 is the correct answer.