Carcass wrote:
In triangle ABC, the measure of angle B is 90°, the length of side AB is 4, and the length of side BC is x. If the length of hypotenuse AC is between 4 and 8, which of the following could be the value of x ?
Indicate \(all\) such values.
❑ 1
❑ 2
❑ 3
❑ 4
❑ 5
❑ 6
I would solve the question by testing each choice.
A) x = 1
The Pythagorean theorem tells us that 4² + 1² = hypotenuse²
Solve to get: Hypotenuse = √17
Since √17 is between 4 and 8, x COULD equal 1
B) x = 2
The Pythagorean theorem tells us that 4² + 2² = hypotenuse²
Solve to get: Hypotenuse = √20
Since √20 is between 4 and 8, x COULD equal 2
C) x = 3
The Pythagorean theorem tells us that 4² + 3² = hypotenuse²
Solve to get: Hypotenuse = √25
Since √25 is between 4 and 8, x COULD equal 3
D) x = 4
The Pythagorean theorem tells us that 4² + 4² = hypotenuse²
Solve to get: Hypotenuse = √32
Since √32 is between 4 and 8, x COULD equal 4
E) x = 5
The Pythagorean theorem tells us that 4² + 5² = hypotenuse²
Solve to get: Hypotenuse = √41
Since √41 is between 4 and 8, x COULD equal 5
F) x = 6
The Pythagorean theorem tells us that 4² + 6² = hypotenuse²
Solve to get: Hypotenuse = √52
Since √52 is between 4 and 8, x COULD equal 6
Answer: A, B, C, D, E and F
i checked other posts, but sill could not find answer to my question.
why are not we considering "the sum of two sides should be greater than the third side" in case x = 1 and hypotenuse is between 4 and 8, then even 1 cant be answer because 4+1=5 which can be longer than hypotenuse say hypotenuse is 4.5 which is less than sum (4+1=5) of other two sides. and that violates the property of "the sum of two sides should be greater than the third side"
can you pls explain.