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=45 and c+b=81, find the value of c.

Sure, here's how you can solve this problem:

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 = 45. So, we can substitute this value into the equation:

c² = 45² + b² c² = 2025 + b²

Step 3: We are also given that c + b = 81. We can rearrange this equation to find b in terms of c:

b = 81 - c

Step 4: Now, we can substitute b = 81 - c into the equation from step 2:

c² = 2025 + (81 - c)²

Step 5: Simplify this equation and solve for c:

c² = 2025 + 6561 - 162c + c² 0 = 6561 - 162c - 2025 0 = 4536 - 162c

Step 6: Solve for c:

162c = 4536 c = 4536 / 162 c = 28

So, the length of the hypotenuse (c) is 28 units.