A new youth activity center is being built in oak valley. the perimeter of the rectangular playing field is 332 yards. the lengt
2 answers:
In this question, it is given that
A new youth activity center is being built in oak valley. the perimeter of the rectangular playing field is 332 yards. the length of the field is 5 yards less than double the width.
Let the width is x yards . And length is 5 yards less than double the width, so length is (2x-5) yards .
Perimeter is the sum of all sides, that is
So the width is 57 yards and length is
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Answer:
Part A)
Part B) option 1,option 4
Step-by-step explanation:
Part A) Derive the formula for the area of a sector
we know that
The area of circle is equal to
The area of circle subtends a central angle of 360 degrees
so
using proportion
Find out the area of a sector by a central angle of ∅ degrees
Part B) Verify each case
case 1) we have
radius = 5 cm
angle = 120°
area = 26.2 cm 2
Find the area of the sector and then compare with the value of the given area
assume
substitute the given values
so
The given value of area is correct
case 2) we have
radius = 4 cm
angle = 105°
area = 16.7 cm 2
Find the area of the sector and then compare with the value of the given area
assume
substitute the given values
so
The given value of area is not correct
case 3) we have
radius = 6 cm
angle = 85°
area = 23.7 cm 2
Find the area of the sector and then compare with the value of the given area
assume
substitute the given values
so
The given value of area is not correct
case 4) we have
radius = 7
angle = 75°
area = 32.1 cm 2
Find the area of the sector and then compare with the value of the given area
assume
substitute the given values
so
The given value of area is correct