Divide 12 into two parts such that the sum of their square is 74?
well, the only choices are
64 and 10 - nope
49 and 15 - nope
36 and 36 - yep
6+6=12
6^2+6^2 = 72
Grgf
5 square + 7 square =74.5+7=12. So these are the 2 parts.
To divide 12 into two parts such that the sum of their squares is 74, we can use algebra to set up the problem and solve it.
Let's assume one part is x and the other part is 12 - x.
According to the problem, the sum of their squares is 74:
x^2 + (12 - x)^2 = 74
To find the solution, we need to solve this quadratic equation.
Expanding the equation and simplifying:
x^2 + (144 - 24x + x^2) = 74
2x^2 - 24x + 144 = 74
Subtracting 74 from both sides of the equation:
2x^2 - 24x + 70 = 0
Dividing both sides of the equation by 2 to simplify:
x^2 - 12x + 35 = 0
Now we can solve this quadratic equation. Factoring or applying the quadratic formula will give us the values of x.
Factoring the quadratic equation:
(x - 7)(x - 5) = 0
Setting each factor equal to zero:
x - 7 = 0 or x - 5 = 0
Solving for x:
x = 7 or x = 5
So the two parts that divide 12 such that the sum of their squares is 74 are 7 and 5.