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
IRISSAK [1]
3 years ago
15

Given: KLMN is a trapezoid m∠N = m∠KML ME ⊥ KN , ME = 3√5 , KE = 8, LM:KN = 3:5 Find: KM, LM, KN, Area of KLMN

Mathematics
2 answers:
lora16 [44]3 years ago
8 0
Q1)Find KM
As ME is perpendicular to KN, ∠KEM is a right angle
Therefore ΔKEM is a right angled triangle 
KE is given and and ME is also given, we need to find KM
for this we can use Pythogoras' theorem where the square of hypotenuse is equal to the sum of the squares of the adjacent sides.
KM² = KE² + ME²
KM² = 8² + (3√5)²
       = 64 + 9x5
KM = √109
KM = 10.44

Q2)Find LM
It is said that ratio of LM:KN is 3:5
Therefore if we take the length of one unit as x
length of LM is 3x
and the length of KN is 5x
KN is greater than LM by 2 units 
If we take the figure ∠K and ∠N are equal. 
Since the angles on opposite sides of the bases are equal then this is called an isosceles trapezoid. So if we draw a line from L that cuts KN perpendicularly at D, ΔKEM and ΔLDN are congruent therefore KE = DN
since KN is greater than LM due to KE and DN , the extra 2 units of KN correspond to 16 units 
KN = LM + 2x 
2x = KE + DN
2x = 8+8
x = 8
LM = 3x = 3*8 = 24

Q3)Find KN 
Since ∠K and ∠N are equal, when we take the 2 triangles KEM and LDN, they both have;
same height ME = LD perpendicular distance between the 2 parallel sides 
same right angle when the perpendicular lines cut KN
∠K = ∠N 
when 2 angles and one side of one triangle is equal to two angles and one side on another triangle then the 2 triangles are congruent according to AAS theorem (AAS). Therefore KE = DN 
the distance ED = LM
Therefore KN = KE + ED + DN
 since ED = LM = 24
and KE + DN = 16
KN = 16 + 24 = 40
another way is since KN = 5x and x = 8
KN = 5 * 8 = 40

Q4)Find area KLMN
Area of trapezium can be calculated using the following general equation 
Area = 1/2 x perpendicular height between parallel lines x (sum of the parallel sides)
where perpendicular height - ME
2 parallel sides are KN and LM
substituting values into the general equation
Area = 1/2 * ME * (KN+ LM) 
         = 1/2 * 3√5 * (40 + 24)
         = 1/2 * 3√5 * 64
         = 3 x 2.23 * 32
         = 214.66 units²


finlep [7]3 years ago
3 0

Answer:

( On Credit Recovery )

KN = 15 units

NM = 20 units

Step-by-step explanation:

You might be interested in
55g as a percentage of 2.2kg
Evgesh-ka [11]

Answer:

2.5%

2.2kg=2200g

<u>\frac{x}{100}  \times 2200 = 55 \\ 22x = 55 \\ x = 2.5\%</u>

3 0
3 years ago
Another one another one...........
USPshnik [31]

Answer:

B

Hope it helped you out

Tysm

4 0
3 years ago
What is the vertex of the graph shown below? Write your answer in the form<br> (x,y).
Leni [432]

Answer:(-3,-1.5)

Step-by-step explanation: the vertex is the point then the line starts to bend. that would be (-3,-1.5).

3 0
2 years ago
Which function is the inverse of f(x)= B^X
Scrat [10]

Answer:

Step-by-step explanation:

Let's retype that as y = b^x.  The inverse of this function is log    y = x  

                                                                                                        b

which you could also write as  y = ln     x

                                                             b

If you had y = e^x, the inverse function would be y = ln x.

Note that if you let ln x be the input to y = e^x, the result would be just 'x,' which confirms that these two functions are inverses of one another.

8 0
3 years ago
Help please thank you
mash [69]

Answer:

1/5

Step-by-step explanation:

Scale factor= Image/Object

Figure C

_______(Take any of the sides of both figures)

Figure B

Scale factor= 1.5 1

___ = __

7.5 5

5 0
3 years ago
Read 2 more answers
Other questions:
  • A right triangle has a hypotenuse of 155 centimeters and a leg of 124 centimeters. Which of these is the length of the other leg
    11·1 answer
  • What is the radius of a circle given by the equation x2 + y2 – 2x + 8y – 47= 0?
    5·2 answers
  • Mr. rameriz is buying square stones to cover his patio. The patio measures 7.5 feet by 9 deer. Each stone is 6 inches on a side.
    15·1 answer
  • Use the definition of continuity to determine whether f is continuous at a. f(x) = 5x+5 a = -5 Question
    10·2 answers
  • Help please ::
    11·1 answer
  • 1. Line that crosses through (6,4) with a slope of -23
    7·2 answers
  • 101 E Victoria Ct, Greenville, NC 27858 my address from mr beast
    12·2 answers
  • The figure below is the graph of the dimensions of a rectangle whose adjacent side lengths exhibit Inverse Variation (1,4) (2,2)
    6·1 answer
  • ASAP!!! I NEED HELP geometry/trigonometry please
    13·1 answer
  • On Monday, Duncan skateboard shop received its first shipment of skateboards. Duncan sold 12 skateboards that day. On Thursday,
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!