Question

Decide if the following statement is

valid or invalid.
If the base of a triangle is 3 and its
height is 4, then its area is 6. This
triangle has an area of 6, so its
base is 3 and its height is 4.

Answer 1

The given statement is invalid because it doesn't align with the formula for the area of a triangle.

Step-by-step explanation:

The given statement is invalid. The formula for the area of a triangle is 1/2 × base × height. If the base of a triangle is 3 and its height is 4, the area would be 1/2 × 3 × 4 = 6. However, the statement claims that this triangle with an area of 6 has a base of 3 and a height of 4, which doesn't align with the formula. Therefore, the given statement is invalid.

Answer 2

Step-by-step explanation:

the area of a triangle is base times height divided by 2.

A = (b × h) / 2

so, when b = 3 and h = 4, then

A = (3 × 4) / 2 = 12 / 2 = 6

correct.

now the other way around

we know the area (6).

=> 6 = (b × h) / 2

=> 12 = b × h

well, b=3, h=4 is one possible solution for this.

but so is e.g. b=2, h=6, or b=12, h=1, or ...

and that is just the natural numbers. then there are rational numbers and so on.

therefore there is an infinite set of possible (b, h) pairs that satisfy the equation 12 = b × h.

therefore the statement that we can conclude out of a given triangle area of 6 that b must be then 3 and h must be 4 is wrong.

simple - it is one equation with 2 variables and has therefore usually not just one solution.