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2 answers:
Step-by-step explanation:
First , Split the given shape into two parts : Trapezium and rectangle :
Here , 18 m and 11 m are the opposite parallel side and (15-8) = 7m is the height of the trapezium.
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Area of trapezium = 101.5 m²
In rectangle , 18 m is the length and 8 m is the width.
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Area of a rectangle = 144 m
Now , Finding total area of given shape :
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Answer: x = 15, ∠K = 45.7°, ∠L = 45.7°, ∠M = 88.6°
<u>Step-by-step explanation:</u>
Since ∠K ≅ ∠L, then ΔKLM is an isoceles triangle with base KL
KM ≅ LM
3x + 23 = 7x - 37
23 = 4x - 37
60 = 4x
15 = x
KM = LM = 3x + 23
= 3(15) + 23
= 45 + 23
= 68
KL = 9x - 40
= 9(15) - 40
= 135 - 40
= 95
Next, draw a perpendicular bisector KN from K to KL. Thus, N is the midpoint of KL and ΔMNL is a right triangle.
- Since N is the midpoint of KL and KL = 95, then NL = 47.5
- Since ∠N is 90°, then NL is adjacent to ∠l and ML is the hypotenuse
Use trig to solve for ∠L (which equals ∠K):
cos ∠L =
cos ∠L =
∠L = cos⁻¹
∠L = 45.7
Triangle sum Theorem:
∠K + ∠L + ∠M = 180°
45.7 + 45.7 + ∠M = 180
91.4 + ∠M = 180
∠M = 88.6
Answer:
Let total number of dog and cat population in animal shelter be x.
As per the statement:
An animal shelter has 9 puppies.
⇒ Total number of puppies = 9
It is also given that if the puppies are 36% of the total dog and cat population.
⇒
or
By cross multiply we get;
Divide both sides by 36 we get;
Therefore, total number of dogs and cat population in animal shelter are 25