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gavmur [86]
3 years ago
13

50 POINTS!!! In rectangle ABCD, AB = 6 cm, BC = 8 cm, and DE = DF. The area of triangle DEF is one-fourth the area of rectangle

ABCD. What is the length in centimeters of segment EF? Express your answer in simplest radical form.

Mathematics
2 answers:
aalyn [17]3 years ago
6 0

Answer:

EF=4\sqrt{3}

Step-by-step explanation:

In rectangle ABCD, AB = 6, BC = 8, and DE = DF.

ΔDEF is one-fourth the area of rectangle ABCD.

We want to determine the length of EF.

First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:

A_{\text{rect}}=8(6)=48\text{ cm}^2

The area of the triangle is 1/4 of this. Therefore:

\displaystyle A_{\text{tri}}=\frac{1}{4}(48)=12\text{ cm}^2

The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:

\displaystyle 12=\frac{1}{2}(DE)(DF)

Since DE = DF:

24=DF^2

Thus:

DF=\sqrt{24}=\sqrt{4\cdot 6}=2\sqrt{6}=DE

Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:

(DE)^2+(DF)^2=(EF)^2

Therefore:

(2\sqrt6)^2+(2\sqrt6)^2=EF^2

Square:

24+24=EF^2

Add:

EF^2=48

And finally, we can take the square root of both sides:

EF=\sqrt{48}=\sqrt{16\cdot 3}=4\sqrt{3}

Black_prince [1.1K]3 years ago
4 0

Answer:

4\sqrt3

Step-by-step explanation:

we know that the area is 6 * 8 = 48 cm^2. because triangle DEF is one fourth of that, triangle DEF's area would be 12.

to find the hypotenuse of triangle DEF, we would first need to find the bases (which have equal lengths). 1/2 * b * b = 12, so b^2 = 24. using the pythagorean theorem, we have \sqrt24 + \sqrt24 = h^2 which means h is the sqrt of 48. simplified, we have 4\sqrt3.

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mariarad [96]

300 messages would have to be sent or received in order for the plan to cost same each month.

Step-by-step explanation:

Given,

Cost per month = $30

Per text sent or received charges = $0.10

Let,

x be the number of texts sent or received.

A(x) = 0.10x+30    

A comparable plan costs = $60 per month

Text messages are unlimited.

B(x) = 60

For the two plans to cost equal;

A(x) = B(x)

0.10x+30=60\\0.10x=60-30\\0.10x=30

Dividing both sides by 0.10

\frac{0.10x}{0.10}=\frac{30}{0.10}\\x=300

300 messages would have to be sent or received in order for the plan to cost same each month.

Keywords: function, addition

Learn more about functions at:

  • brainly.com/question/2860697
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#LearnwithBrainly

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3 years ago
Mel's Furniture received an invoice dated September 27 for 5 bedroom sets at $3,000 each. The invoice indicated a chain discount
LenKa [72]

Answer: $12,916.70

Step-by-step explanation:

Given the following:

Invoice received :

Bedroom set = 5

Cost per set = $3,000

Chain discount = 5/8/3

Freight cost = $200

If Mel pays within the discount period:

Chain discount given = 5/8/3

Therefore, net equivalent price rate equals:

(1 - 0.05) × (1 - 0.08) × (1 - 0.03) =

0.95 × 0.92 × 0.97 = 0.84778

Net price = total cost × 0.84778

($3000 × 5) × 0.84778

$15000 × 0.84778 = $12,716.7

Net equivalent price + FOB Shipping

$12,716.7 + $200 = $12,916.70

5 0
3 years ago
A sidewalk forms the diagonal of a square park. The sidewalk is 30 meters long. To the nearest tenth of a meter, how long are th
PtichkaEL [24]
<span> <span>We can use the Pythagorean Theorem (A² + B² = C²) to solve for the lengths of the sides. We know that the diagonal, C, is 30 meters long, so C² = 900 meters. We know that since the park is square, A² + B² = 2A² = 2B²

900 = 2A²

A^2 = 450

Taking the square root of 450, we find that the lengths of A and B are roughly 21.2 meters.</span> </span>
8 0
3 years ago
Read 2 more answers
Just question eleven .
gregori [183]
I’m pretty sure a is always and b is sometimes.
7 0
2 years ago
Ariel made cupcakes to sell. 2/3 of them were chocolate chip,25% of the reminder was strawberry and the rest were 90 vanilla cup
Anton [14]

Answer:

Let x be the total number of cupcakes.

Chocolate chips =

\frac{2}{3} x

Strawberry =

\frac{1}{4}  \times  \frac{1}{3}  \\  =  \frac{1}{12} x

Vanilla =

x -  \frac{2}{3} x -  \frac{1}{12}x \\  =  \frac{1}{3} x -  \frac{1}{12} x \\   =  \frac{1}{4} x

given

\frac{1}{4} x = 90

x = 90 \div  \frac{1}{4}  \\  = 90 \times 4 \\  = 360

a)Number of Chocolate chip Cupcakes =

\frac{2}{3}  \times 360 \\  = 240

b)Number of Strawberry cupcakes =

\frac{1}{12}  \times 360 \\  = 30

8 0
3 years ago
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