Question

if possible, use the law of detachment to make a conclusion. if it is not possible to make a conclusion, tell why. if a square has side length 5 cm, then it has area 25 cm². square abcd has area 25 cm². choose the correct answer below. a. it is not possible to make a conclusion using the law of detachment because the second statement does not match the conclusion of the given conditional statement. b. the conclusion is square abcd has perimeter 5 cm. c. the conclusion is the square has side length 5 cm. d. no conclusion is possible because the hypothesis given is not the same as the hypothesis of the given conditional statement.

Explanation:

Step1: Recall the Law of Detachment

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion is true. The conditional statement here is: If a square has side - length 5 cm, then it has area 25 cm². The hypothesis is "a square has side - length 5 cm" and the conclusion is "it has area 25 cm²".

Step2: Analyze the given statements

We are given that a square has side - length 5 cm. Since the hypothesis of the conditional statement is met, we can apply the Law of Detachment.

Step3: Determine the conclusion

When the side - length of a square is \(s = 5\) cm, the area of the square \(A=s^{2}=5^{2}=25\) cm². So the conclusion that the square has area 25 cm² is valid.

Answer:

C. The conclusion is the square has side length 5 cm.