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
