To find: The concrete bags required to build patio.
The number of concrete bags required to construct the patio is 43.
Given data:
The dimensions of the patio are triangular sides of length 8 feet, 11 feet, and 15 feet. And thickness 0.5 ft. One bag of cement takes 0.33 cubic foot of concrete.
Method/Formula used:
The ‘Law of Cosines’ states for a
The area of triangle ABC is
Calculations:
The construction volume of triangular patio ABC with sides AB or c equals 15 feet, BC or
The volume of concrete used to make the patio is
Substitute 8 for a , 11 for b and 15 for c in result (1),
Substitute
Thus, the area of the triangular base of the patio is 28.15 sq. feet.
Substitute 28.15 as the area of triangle ABC and 0.5 foot as the height of the patio in result (3), the volume V of concrete used to make the patio is,
Thus, the volume of concrete used for constructing the patio is
Since, a concrete bag contains 0.33 cubic feet of the concrete, therefore, the number N of concrete bags required to construct the patio is,
Substitute
Therefore, 43 concrete bags are required to construct the patio.
Chapter 9 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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