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.
Answer:
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 centimeters
- Side D-E = 10 centimeters
- Side F-E = 8 centimeters
Now,
- the midpoint of side F-D is A ⇒ 6/2 = 3cm
- the midpoint of side D-E is B ⇒ 10/2 = 5cm
- the midpoint of side F-E is C ⇒ 8/2 = 4cm
These values suggest that
- Side F-A ⇒ 3 cm = Side B-C ⇒ 3cm
- Side E-B ⇒ 5 cm = Side A-C ⇒ 5cm
- Side 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.
The value of p and q is 2 , -8 , The nth term of the series is given by 3 * n² + n-2 , the 40th term is 4838 .
<h3>What is a quadratic Sequence ?</h3>
A sequence which has n term in its sequence , The difference of the consecutive number is not same , its second difference is same.
The sequence is given as 7; p; -3;q;...
for a linear pattern
7-p = p- (-3) = -3-q
2p = 4
p = 2
and
2+3 = -3 -q
5 +3 = -q
q = -8
The value of p and q is 2 , -8
A quadratic sequence is defined as 2; 12; 28; 50
The next two terms are 77 and 112.
3. The T40 of the sequence is
The nth term of the series is given by
3 * n² + n-2
therefore 40th term is
3 *40² + 40-2
3 *1600 +38
4838
Therefore the 40th term is 4838 .
To know more about Quadratic Sequence
brainly.com/question/22412845
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What! i dont know this math yet:(
Ratios are like fractions. 5:6 is the same as 5/6.