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Evan is making a table that will be created in the shape of the figure below. The table top is a triangle attached to a rectangle. To purchase the right amount of paint, he needs to know the area of the table top. He can only spend $10 on paint, which is enough to cover 150 ft2 of surface area. What is the maximum length of the base of the rectangle he can build?

Verified Answer :

Given:
Height = 4 feet
Base = 6 feet
so, 
Area of triangle = 1/2 x b x h 
                         = 1/2 x 6 x 4 
                         = 12 feet squared 
 
Area of rectangle = length x width 
                             = a x 6 
                             = 6 a
 
Total area = 6a + 12 
The maximum area = 150 ft^2 
Using inequality
6a +12 must be less than or equal to 150 
6a less than or equal to 150-12 
6a less than or equal to 138 
a less than or equal to 138/6 
a less than or equal to 23 
Hence,
The length of the rectangle should be less than or equal to 23 feet.

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