Mathematics, 24.06.2021 18:20 brapmaster764

Points A, B, and C are midpoints of the sides of right triangle DEF. Triangle A B C is inside triangle D E F. Point A is the midpoint of side F D, point B is the midpoint of side D E, point C is the midpoint of side F E. Angles D F E and A B C are right angles. The length of D E is 10 centimeters, the length of F D is 6 centimeters, and the length of F E is 8 centimeters. Which statements are true? Select three options. (The formula for the area of a triangle is A = One-halfbh.)

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Answer from: weeblordd

Complete question:

Points A, B, and C are midpoints of the sides of right triangle DEF. Triangle A B C is inside triangle D E F. Point A is the midpoint of side F D, point B is the midpoint of side D E, point C is the midpoint of side F E. Angles D F E and A B C are right angles. The length of D E is 10 centimeters, the length of F D is 6 centimeters, and the length of F E is 8 centimeters. Which statements are true? Select three options. (The formula for the area of a triangle is A = One-halfbh.)

BC = 6 cm AC = 5 cm BA = 4 cm The perimeter of triangle ABC = 12 cm. The area of triangle ABC is One-third the area of triangle DEF.

2. A-C = 5 cm

3. B-A = 4 cm

4. The perimeter of triangle A-B-C = 12 cm.

Step-by-step explanation:

First, picture a triangle formed by points D-E-F.

Side F-D = 6 centimetersSide D-E = 10 centimetersSide F-E = 8 centimeters

Now,

the midpoint of side F-D is A ⇒ 6/2 = 3cmthe midpoint of side D-E is B ⇒ 10/2 = 5cmthe midpoint of side F-E is C ⇒ 8/2 = 4cm

These values suggest that

Side F-A ⇒ 3 cm = Side B-C ⇒ 3cmSide E-B ⇒ 5 cm = Side A-C ⇒ 5cmSide F-C = E-C ⇒ 4cm = Side A-B ⇒ 4cm

The perimeter of the interior triangle ABC = 3cm + 5cm + 4cm = 12 cm

The total area of the interior triangle ABC is 1/4 the area of triangle DEF. You can see in the picture that there are four equal triangles inside DEF.

Points A, B, and C are midpoints of the sides of right triangle DEF. Triangle A B C is inside triang

Answer from: Quest

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that runner b is moving at a slower rate."

Answer from: Quest

The answe maybbe

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