Answer: Her solution is incorrect. The hypotenuse is 53 units
Step-by-step explanation: The error occurred when she quoted the Pythagorean theorem. She added up both sides and squared them and made the answer equal to the square of the hypotenuse. She was supposed to have squared them first, before adding up.
The Pythagorean (or Pythagoras) theorem states that the sum of the squares of two sides of a right angled triangle equals the square of the hypotenuse of the triangle. That is, in triangle ABC, if the hypotenuse is given as line AC, the Pythagoras theorem states that
AC^2 = AB^2 + BC^2
Where AC is the hypotenuse and AB and BC are the other two sides.
In Nadia’s solution, if the hypotenuse is given as 73, and the other two sides are 28 and 45, then the Pythagorean theorem properly expressed would be as follows;
73^2 = 28^2 + 45^2
5329 = 784 + 2025
5329 ≠ 2809
As we have determined, writing out the expression as
73^2 = (28 + 45)^2 is very incorrect as this is not the Pythagorean theorem and of course, the triangle cannot have 73 as its hypotenuse as we have determined by properly writing out the Pythagorean theorem.
The correct solution is as follows;
AC^2 = AB^2 + BC^2
AC^2 = 28^2 + 45^2
AC^2 = 784 + 2025
AC^2 = 2809
Add the square root sign to both sides of the equation
AC = 53
Therefore, the hypotenuse is 53 units
