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

Since the base and height of the triangle is given , lets find its area first.
A = 1/2*b*h
= 1/2*6*4
= 12 ft^2
Now the length of the rectangle is to be found. Width is given to be 6.
Area of rectangle ,
A = l*b
= x*6
=6x
Total area to be painted = 6x + 12
The maximum area he can paint = 150 ft^2
We get an inequality equation here :
6x+12 <= 150
6x <= 150-12
6x <= 138
x <= 138/6
x<= 23
So , x or the length of the rectangle should be less than or equal to 23 feet.