Question

the pythagorean theorem > section exercises 7.3 > exercise 9
the length of the leg was substituted for the wrong variable.
the length of the hypotenuse was substituted for the wrong variable.
the square root of 674 has not been simplified.
select and order the steps to correct the error
a² + b² = c²
7² + 25² = c²
674 = c²
√674 = c

Explanation:

Step1: Identify the legs and hypotenuse

In a right - triangle, the Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Given legs of lengths 7 ft and 25 ft, we should have $a = 7$, $b = 25$. The error is that the lengths of the legs were substituted for the wrong variables in the setup of the Pythagorean theorem.

Step2: Correct substitution

The correct substitution into $a^{2}+b^{2}=c^{2}$ gives $7^{2}+25^{2}=c^{2}$. Calculate $7^{2}=49$ and $25^{2}=625$. Then $49 + 625=c^{2}$, so $c^{2}=674$.

Step3: Simplify the square - root

Factorize 674: $674=2\times337$. Since 2 and 337 are prime numbers, $\sqrt{674}$ is already in simplest radical form.

Answer:

The length of the leg was substituted for the wrong variable.