1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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.

You might be interested in
What is  5.63×10−6in decimal form?a. 0.00000563 b. 0.000000563 c.5,630,000d. 56,300,000
Lelu [443]

5.63 \times  {10}^{ - 6}

To convert into decimal, move the decimal to the left by 6 positions.

It will be 0.00000563

Answer is A.
3 0
3 years ago
*Please answer before 5:45! I'll award brainliest!*
FromTheMoon [43]

Answer:

A

Step-by-step explanation:

Vertical angles are angles that are formed by 2 lines and are directly accross from each other. They do not share a ray, however they are always the same number of degrees.

so then the answer would be A, ∠ERT and ∠MRC since they are directly across from each other.

4 0
3 years ago
Pls help me with this question
maksim [4K]

top left

is not

Step-by-step explanation:

5 0
1 year ago
Read 2 more answers
Please help me with this homework question. No silly answers please and no bots! I will mark brainliest to whoever gets all them
MatroZZZ [7]

Answer:

The formula for the area of the triangle is:

\displaystyle A=24x^2

When <em>x</em> = 3, the area is 216 square centimeters.

When <em>x </em>= 2.4, the area is 138.24 square centimeters.

And when <em>x</em> = 5, the hypotenuse of the triangle is 50 centimeters.

Step-by-step explanation:

We are given a right triangle with a height of 8<em>x</em> and a base of 6<em>x</em>.

The area of a triangle is given by the formula:

\displaystyle A=\frac{1}{2}bh

So, by substitution:

\displaystyle A=\frac{1}{2}(8x)(6x)=24x^2

When <em>x </em>= 3, the area will be:

\displaystyle A(3)=24(3)^2=216\text{ cm}^2

And when <em>x</em> = 2.4, the area will be:

A(2.4)=24(2.4)^2=138.24\text{ cm}^2

When <em>x </em>= 5, the height will be 8(5) = 40 cm and the base will be 6(5) = 30 cm.

By the Pythagorean Theorem:

a^2+b^2=c^2

So:

(40)^2+(30)^2=c^2

The hypotenuse will be:

c=\sqrt{1600+900}=\sqrt{2500}=50\text{ cm}

3 0
2 years ago
What is the answer to: 20*5 thank you very much
Digiron [165]
20 times 5 is 100. We can multiply 2*5 and get 10, then add another zero to make it easier. 
3 0
3 years ago
Other questions:
  • Find parametric and symmetric equations of the line through the point (2,1,0) and perpendicular to the plane 5x-3y + 4z = 15
    5·1 answer
  • Convert the following equation into simultaneous equation and solve
    8·1 answer
  • Jon's grades from reading class are shown below.
    5·1 answer
  • I need the complete answer to this problem, please circle the final answer and what I should write
    9·1 answer
  • A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is
    7·1 answer
  • The principal. Ms kennedy and the chairman were at the meeting how many persons were at the meeting
    14·2 answers
  • Sarafina had 34 out of 99 hits when she was at bat during the soft ball season. What was her batting average? (use bar notation
    8·1 answer
  • Can someone please help me with this
    12·1 answer
  • What pecent of 50 is 7
    6·2 answers
  • A uniform density curve goes from negative 5 to positive 1.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!