25.09.2020

Abc is an equilateral triangle. BC is extended to D so that CAD = 25. What is the measure of ADC

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Mathematics

Abc is an equilateral triangle with sides equal to 2 cm. bc is extended its own length to d, and e is the midpoint of ab. ed meets ac at f. find the area of the quadrilateral befc in square centimeters in simplest radical form.

Step-by-step answer

P Answered by Specialist

$\frac{2\sqrt3}{3}$ cm^2

Step-by-step explanation:

Since $\triangle ABC$ is equilateral triangle, then $\angle A = \pi /3$

So,

$S_{\triangle ABC} = \frac{2 * 2 * sin(\pi /3)}{2} = \frac{2 * 2 * \sqrt{3}/2}{2} = \sqrt{3}$ cm^2

Then we need to find $S_{\triangle AEF}$ which can be computed by finding length_AF.

Let's call x = length_AF.

By Menelao's Theorem,

$\frac{BE*x*CD}{AE*(2-x)*BD} = \frac{1*x*2}{1*(2-x)*4} = 1$

⇒ x = 4/3 cm

Thus,

$S_{\triangle AEF} = \frac{1 * x * sin(\pi /3)}{2} = \frac{1 * 4/3 * \sqrt{3}/2}{2} = 1/\sqrt{3}$ cm^2

To find the area of quadrilateral BEFC , we have to subtract $S_{\triangle AEF}$ from $S_{\triangle ABC}$

Hence,

$S_{BEFC} = S_{\triangle ABC} - S_{\triangle AEF} = \sqrt3 -1/\sqrt3 = \frac{2\sqrt3}{3}$ cm^2

Mathematics

Step-by-step answer

P Answered by Specialist

$\frac{2\sqrt3}{3}$ cm^2

Step-by-step explanation:

Since $\triangle ABC$ is equilateral triangle, then $\angle A = \pi /3$

So,

$S_{\triangle ABC} = \frac{2 * 2 * sin(\pi /3)}{2} = \frac{2 * 2 * \sqrt{3}/2}{2} = \sqrt{3}$ cm^2

Then we need to find $S_{\triangle AEF}$ which can be computed by finding length_AF.

Let's call x = length_AF.

By Menelao's Theorem,

$\frac{BE*x*CD}{AE*(2-x)*BD} = \frac{1*x*2}{1*(2-x)*4} = 1$

⇒ x = 4/3 cm

Thus,

$S_{\triangle AEF} = \frac{1 * x * sin(\pi /3)}{2} = \frac{1 * 4/3 * \sqrt{3}/2}{2} = 1/\sqrt{3}$ cm^2

To find the area of quadrilateral BEFC , we have to subtract $S_{\triangle AEF}$ from $S_{\triangle ABC}$

Hence,

$S_{BEFC} = S_{\triangle ABC} - S_{\triangle AEF} = \sqrt3 -1/\sqrt3 = \frac{2\sqrt3}{3}$ cm^2

Mathematics

Imran is paid ?286 per week Every week he puts 20% of his wage into a savings account How much does he put into his savings each week

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P Answered by PhD

The answer is in the image

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

Step-by-step answer

P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

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Deanna gets 3 problems incorrect on a math quiz. Her score is 85%. How many questions are on the quiz?

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P Answered by PhD

The answer is in the image

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Anthony received $150 for his birthday this year. This was $10 less than half the amount he received last year. How much money did Anthony receive for his birthday last year?

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The answer is in the image

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An online media service offers video and music downloads. Each download of a song costs $1. Each download of a video costs 5 times as much as the song download. You have a credit of $70. How many songs can you purchase after buying 12 videos?

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The answer is in the image

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In a parking lot, for every 8 cars there are 7 trucks. What is the ratio of cars to trucks? A)7 : 8 B)8 : 7 C)8 : 15 D)15 : 8

Step-by-step answer

P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

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Step-by-step answer

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Abc is an equilateral triangle. BC is extended to D so that CAD = 25. What is the measure of ADC

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