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babymother [125]
3 years ago
15

Point E is the midpoint of side BC of parallelogram ABCD (labeled counterclockwise) and AE ∩ BD =F. Find the area of ABCD if the

area of △BEF is 3 cm^2.

Mathematics
1 answer:
tester [92]3 years ago
6 0

Answer:

The area of ABCD is 36 cm².

Step-by-step explanation:

Given information: ABCD is a parallelogram, E is the midpoint of BC and AE ∩ BD=F.

In triangle EBF and ADF

\angle FBE=\angle FDA          (Alternate interior angles)

\angle FEB=\angle FAD          (Alternate interior angles)

\angle BFE=\angle DFA          (Vertically opposite angles)

Therefore triangle EBF and ADF are similar triangles by AA rule.

The sides BC and AD are opposite sides of parallelogram, therefore their lengths are equal. E is midpoint of BC.

\frac{BC}{AD}=\frac{1}{2}

If a point divides the side of a triangle in m:n, then the line segment between the point and the opposite vertex, divides the area of triangle is m:n.

Therefore the sides of triangle are in proportion of 1:2 and we can say that the point F divides the line EA and BD in 1:2.

In triangle ABE, the line BF divides the area of triangle is 1:2.

\text{ Area of }\triangle BEF:\text{ Area of }\triangle ABF=1:2

\text{ Area of }\triangle ABF=2\text{ Area of }\triangle BEF

A_{\triangle ABF}=2A_{\triangle BEF}

A_{\triangle ABF}=2\times 3=6

In triangle ABD, the line FA divides the area of triangle is 1:2.

\text{ Area of }\triangle ABF:\text{ Area of }\triangle DFA=1:2

\text{ Area of }\triangle DFA=2\text{ Area of }\triangle ABF

A_{\triangle DFA}=2A_{\triangle ABF}

A_{\triangle DFA}=2\times 6=12

A_{\triangle ABD}=A_{\triangle ABF}+A_{\triangle ADF}

A_{\triangle ABD}=6+12=18

Since AD is a diagonal of the parallelogram, therefore AD divides the area of parallelogram in two equal parts.

A_{\triangle ABCD}=2A_{\triangle ABD}

A_{\triangle ABCD}=2\times 18=36

Therefore the area of ABCD is 36 cm².

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if an amount of $5,000 is deposited into a savings account at an annual interest rate of 5%, compounded monthly, what is the val
Ugo [173]

Answer:

$8,240

Step-by-step explanation:

We are given that,

Principle amount in the savings account, P = $5,000.

Rate of interest, r = 5% = 0.05

Time period, t = 10

Also, the interest is compounded monthly, n = 12

As, we now that the value of the investment is given by P(1+\frac{r}{n})^{nt}

Thus, we have,

Investment Value = 5000(1+\frac{0.05}{12})^{12\times 10}

i.e. Investment Value = 5000(1+\frac{0.05}{12})^{12\times 10}

i.e. Investment Value = 5000(1+0.00417)^{120}

i.e. Investment Value = 5000\times 1.648

i.e. Investment Value = $8,240

Hence, the investment amount after 10 years is $8,240.

5 0
3 years ago
How many unit cubes would it take to completely fill the prism with no gaps between unit cubes?
Lemur [1.5K]

Answer:

72 cubes

Step-by-step explanation:

Top view of the rectangular prism shows the unit cubes arranged in two rows along the length.

In each row number of unit cubes arranged = 9

Right view side of the prism shows the unit cubes arranged in two columns.

Number of unit cubes in each column = 4

Total number of cubes arranged in the prism = (Number of cubes in each row × Number of cubes arranged in two columns) × Number of columns

= (9 × 4) × 2

= 72

Therefore, number of cubes filled completely in the prism with no gaps = 72

6 0
3 years ago
To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin tablets that are similar in
lukranit [14]

Answer: \dfrac{26}{27}

Step-by-step explanation:

Given : To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle containing 9 vitamin tablets that are similar in appearance.

Proportion of success : p=\dfrac{6}{9}=\dfrac{2}{3}

Sample size taken by customs official : n= 3

Let x be a binomial variable that represents the tablets in the bottle.

Using Binomial probability formula :-

P(X=x)=^nC_xp^x(1-p)^{n-x}

The probability that the traveler will be arrested for illegal possession of narcotics =P(x\geq1)=1-P(x=0)

1-^3C_0(\dfrac{2}{3})^0(1-\dfrac{2}{3})^3\\\\=1-(1)(1)(\dfrac{1}{3})^3\ [\becuase ^nC_0=1]\\\\=1-\dfrac{1}{27}=\dfrac{26}{27}

Hence, the probability that the traveler will be arrested for illegal possession of narcotics = \dfrac{26}{27}

8 0
3 years ago
Plz Help me with this question
aivan3 [116]

Answer:

The Equivalent Resistance are 5ohms

hope this helps!

5 0
3 years ago
Please help if you can!
Dima020 [189]

Answer:

m' (-2, 4)

n' (-2, 1)

o' (3, 1)

p' (3, 4)

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
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