Question

Lindsie is painting on a canvas with dimensions of 3 ft by 4 ft. She wants to make a display model for a gallery that has twice the area of the original. How much should she increase the length and width by, if she wants to increase them by the same amount? Round your answer to the nearest tenth.
A. 10.4 feet
B. 1.4 feet
C. 3.4 feet
D. 8.4 feet

Answer 1

Answer:

B. 1.4 feet

Step-by-step explanation:

Lindsie is painting on a canvas of 3 ft by 4 ft. She wants to make a display model for a gallery that has twice the area of the original .

The painting on the canvas has the dimension 3 ft by 4 ft . The area can be calculated as follows :

since it is a rectangle,

area = Lb

area = 3 × 4

area = 12 ft²

The new gallery display will have twice the area of the painting on canvas

12 × 2 = 24 ft²

If she wants to increase the length and the width by the same amount the product of the new width and length will be equal or closest to 24 ft²

let x be the same value we are adding

(x + 3)(x + 4) = 24

x² + 4x + 3x + 12 = 24

x² + 7x + 12 = 24

x² + 7x -12 = 0

using Almighty formula

(-b ±√b² - 4ac)/2a

a = 1

b = 7

c = -12

(-7 ± √49 + 48)/2

(-7 ± √97)/2

(-7 ± 9.8488578018 )/2

(-7 + 9.8488578018) /2 0r (-7 - 9.8488578018) /2

2.8488578018 /2     or  -16.8488578018 /2

1.4244289009 ft    or 8.4244289009 ft

x = 1.4244289009 ft ,  8.4244289009  ft

x = 1.4244289009 ft is the best value

x ≈ 1.4 ft

Answer 2

Given the original dimensions above which is 3ft and 4ft, the area of the painting on a canvass would be 12ft. Since Linda wants to double the area of the display model, this makes the doubled area 24ft. So in order to get this area, Linda should add 1.4 feet to both the length and the width, making the dimensions 4.4ft and 5.4ft. Multiply both and you get 23.76ft or to round it off, 24 feet. Hope this answers the question.