Points A, B, and C are midpoints of the sides of right
triangle DEF
Which statements are true? Select three options. (The
formula for the area of a triangle is A = bh.)
BC = 6 cm
AC = 5 cm
BA = 4 cm
DE = 10 cm
FD = 6 cm
FE = 8 cm
The perimeter of triangle ABC = 12 cm.
The area of triangle ABC is
the area of triangle DEF.​

Respuesta :

Answer:

Ac equals 5

The perimeter of the triangle abc is 12 cm

Ba = 4

Step-by-step explanation:

The correct statements of the triangle are; AC = 5 cm; BA = 4 cm; The perimeter of triangle ABC is 12 cm.

What are the correct statements of the Triangles?

As we know that a, b, and c are midpoints of the sides of right triangle that means midpoint divide the side in equal parts.

Now we have to calculate the sides of triangle ABC by using Pythagoras theorem.

Using Pythagoras theorem in ΔACF :

AC² = FA² + CF²

Thus;

AC² = 3² + 4²

AC = √25

AC = 5

Using Pythagoras theorem in ΔDAB, we have;

BA = √(5² - 3²)

BA = 4 cm

Using Pythagoras Theorem, we have;

CB = √(5² - 4²)

CB = 3 cm

Perimeter of ΔABC = Side AB + Side CB+ Side AC

Perimeter of ΔABC = 4 + 3 + 5

Perimeter of ΔABC = 12 cm

Area of ΔABC = (1/2) * 4 * 3 = 6 cm²

Area of ΔDEF = (1/2) * 8 * 6 = 24 cm²

Area of ΔABC =  (6/24) * Area of ΔDEF

Area of ΔABC = (1/4) * Area of ΔDEF

Read more about Correct Triangle Statements at; https://brainly.com/question/12852445

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