a square + b square = 80 ft (c Square)
Through trial and error I can tell you that 6 squared (36) and 12 squared (44)are what you're solving for, but I just used trial and error to figure it out.
12 square is 144, not 44
a and b can be a combination of many numbers. For instance, if a is =1, then
b= square root of 79.
To solve the equation a^2 + b^2 = 80 ft^2 for the values of a and b, you can use algebraic methods instead of trial and error.
1. Start with the equation: a^2 + b^2 = 80 ft^2.
2. Subtract b^2 from both sides of the equation: a^2 = 80 ft^2 - b^2.
3. Take the square root of both sides: √(a^2) = √(80 ft^2 - b^2).
4. Simplify: a = √(80 ft^2 - b^2).
Now, let's substitute some values for a and solve for b.
1. Let's consider a = 1. Plug in this value into the equation derived above:
1 = √(80 ft^2 - b^2).
2. Square both sides to eliminate the square root: 1^2 = (√(80 ft^2 - b^2))^2.
Simplifying: 1 = 80 ft^2 - b^2.
3. Rearrange the equation to solve for b^2: b^2 = 80 ft^2 - 1.
Therefore, b^2 = 79 ft^2.
4. Take the square root of both sides to find b: b = √(79 ft^2).
Approximating the square root of 79 gives b ≈ 8.89 ft.
So, one possible solution for a and b is a = 1 ft and b ≈ 8.89 ft.
Keep in mind that this is just one solution, and there could be other combinations of a and b that satisfy the equation a^2 + b^2 = 80 ft^2.