Question

If a triangle has sides of lengths 3, 4, and 5 units, then it is

a right triangle. All right triangles have an area equal to one

half the product of the two smaller side lengths.

Which statement is valid, based on deductive reasoning?

OA)

A polygon has an area of 6 square units if it is a

triangle

OB)

A triangle has a perimeter of 12 units if its sides are consecutive

integers.

If a triangle has side lengths 3, 4, and 5 units, then its area is 6

square units.

If a triangle has side lengths 4, 5, and 6 units, then its

area is 10 square units.

OC)

Answer 1

If a triangle has side lengths 3, 4, and 5 units, then its area is 6

Explanation:

Deductive reasoning represents an important form of logical reasoning in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true

we have

If a triangle has side lengths 3, 4, and 5 units, then its area is 6

we know that

1) If triangle has side lengths 3, 4 and 5, then is a right triangle because satisfy the Pythagoras Theorem

2) All right triangles have an area equal to one half the product of the two smaller side lengths

`A=(1)/(2)(a)(b)`

substitute the values

`A=(1)/(2)(3)(4)`

`A=6\ units^2`

therefore

The statement is valid based on deductive reasoning