Question

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?

Answer 1

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.