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? (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.

Answer 1

*The maximum length of the base of the rectangle is 23 ft.*

Given:

Triangle:

height = 6ft

base = 4ft

Rectangle:

length = x

Width = 6 ft

Surface Area = 150ft²

Area of a Triangle = h*b / 2 = (6ft * 4ft) / 2 = 12ft²

Area of a rectangle = Surface Area - Area of a Triangle

A = 150 ft² - 12 ft² = 138 ft²

138 ft² = x * 6ft

138 ft² / 6 ft = x

23 ft = x

23ft is your answer

Answer 2

23 ft

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.