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likoan [24]
3 years ago
14

Did I get these all right

Mathematics
1 answer:
Leviafan [203]3 years ago
3 0
Yep! They are all right! Great job, could write a bit better.... sorry
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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
lora16 [44]
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


8 0
2 years ago
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A theater company is considering raising the price of its tickets. It currently charges $8.50 for each ticket and sells an avera
Licemer1 [7]

Answer:

The answer is c.

Step-by-step explanation:

6 0
3 years ago
A rectangular fish tank has a base that is 8 inches by 7 inches. How much water will it take to fill the tank to a depth of 5 in
Blizzard [7]
V=LWH
L=8
W=7
H=5

V=8*7*5=280 in^3

you need 280 in^3 of water
5 0
3 years ago
What is the answer and how to you solve it as easy as possible​
Gnom [1K]

Answer:

A = 504inch

Step-by-step explanation:

Formula = A = 2(wl + hl + hw)

or A = 2wl + 2lh + 2hw, where w is the width, the l is the length, and the h is the height.

2wl = 6inch × 12inch = 72inch × 2 = 144inch

2lh = 12inch × 10inch = 120inch × 2 = 240inch

2hw = 10inch × 6inch = 60inch × 2 = 120inch

Then add all

144inch + 240inch + 120inch = 504inch

A = 504inch

7 0
3 years ago
Meg made 3 gallons of lemonade for a group of campers. if each camper gets 1 cup of lemonade, how many campers can have lemonade
Sonbull [250]

Answer:

C

Step-by-step explanation:

1 gallon = 16 cups

3 gallons = 48 cups if each camper gets one cup of lemonade, it can serve 48 campers.

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