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? (3 points) An image of a compound shape made up of a rectangle and a triangle is shown. The length of the rectangle is labeled x and the width is labeled 6 feet. The base of the triangle is labeled 4 feet and the height is labeled 6 feet.

23 ft

Step-by-step explanation:

The surface area is known to be 150 square feet. Given the dimensions of this triangle ( 6 feet by 4 feet ) we can determine it's area, therefore calculating the area of this rectangle by subtracting the area of the triangle from the total surface area ( 150 square feet ). The amount of money on paint was there to mislead you, however it gave us the key point of being able to cover a maximum surface area of 150 square feet.

Surface Area = 150 ft²,

Area of Triangle = ( 6 4 ) / 2 = ( 24 ) / 2 = 12 ft²,

Area of Rectangle = Surface Area - Area of Triangle = 150 ft² -  12 ft²

= 138 ft²

Let x = length of the rectangle

138 ft² = x 6 ft,

x = 138 ft² / 6 ft = 23 ft - this is the maximum length of the base of the rectangle he can build.

c

step-by-step explanation:

4

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