Problem 5
Answer: 300 square inches
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Work Shown:
a = 15
b = unknown
c = 25
a^2 + b^2 = c^2
15^2 + b^2 = 25^2
225 + b^2 = 625
b^2 = 625 - 225
b^2 = 400
b = sqrt(400)
b = 20
The rectangle is a = 15 by b = 20 to get an area of ab = 15*20 = 300 square inches.
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Problem 6
Answer:
- Part A) The area = 48 square inches
- Part B) The area = 16*sqrt(2) square inches
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Work Shown:
Part A)
area = base*height/2
area = 8*12/2
area = 96/2
area = 48
Part B)
a^2 + b^2 = c^2
8^2 + b^2 = 12^2
64 + b^2 = 144
b^2 = 144 - 64
b^2 = 80
b = sqrt(80)
b = sqrt(16*5)
b = sqrt(16)*sqrt(5)
b = 4*sqrt(5)
Therefore,
area = base*height/2
area = a*b/2
area = 8*4*sqrt(5)/2
area = 16*sqrt(2)
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Problem 7
Answer: 36 cm
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Work Shown:
area = 81
area = x^2
x^2 = 81
x = sqrt(81)
x = 9
The side lengths of the square are 9 cm each.
P = perimeter
P = 4x
P = 4*9
P = 36
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Problem 8
Answer: 12.5*sqrt(15)
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Work Shown:
The horizontal base of 10 is cut in half to get 5.
a = 5 = horizontal side
b = unknown height
c = 20 = hypotenuse
a^2 + b^2 = c^2
5^2 + b^2 = 20^2
25 + b^2 = 400
b^2 = 400 - 25
b^2 = 375
b = sqrt(375)
b = sqrt(25*15)
b = sqrt(25)*sqrt(15)
b = 5*sqrt(15)
area = base*height/2
area = a*b/2
area = 5*5*sqrt(15)/2
area = 12.5*sqrt(15)