garrettatkinson12 garrettatkinson12
  • 23-08-2021
  • Mathematics
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A trapezoid has a height of 6 ft and a total area of 30 ft^. What are the possible lengths of the bases. Explain your reasoning.

A trapezoid has a height of 6 ft and a total area of 30 ft What are the possible lengths of the bases Explain your reasoning class=

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colinspurdle colinspurdle
  • 23-08-2021
The area of a trapezoid = (a + b)/2 x h
Where a and b are the lengths of the parallel sides and h is the perpendicular distance between them.
When (a + b)/2 x 6 = 30
then (a + b)/2 = 5
a + b = 10

Possible values for (a,b) are (4,6) (3,7) (2,8) (1,9) assuming a < b but (7,3) is also valid.
Any positive real value is possible so (4.8, 5.2) and (0.3, 9.7) are valid

In general {a,b both real: 0
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