Answer:
B. 1.4 feet
Step-by-step explanation:
Let, the amount of increase be 'x' ft.
Since, the length and width of the canvas are 4 ft and 3 ft respectively.
Thus, area of the canvas,
= length × breadth = 4 × 3 = 12 ft²
Since, the area of display model is twice the area of the canvas. We have,
= 2 × ![A_{c}](https://tex.z-dn.net/?f=A_%7Bc%7D)
i.e.
= 2 × 12
i.e.
= 24 ft².
As, the length and width of the canvas are increased by 'x'.
The, length and width of the display model are (x+4) ft and (x+3) ft.
So, we get,
= length × breadth = (x+4) × (x+3) = ![x^{2} +7x+12](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B7x%2B12)
Since,
= 24 ft²
i.e.
= 24
i.e. ![x^{2} +7x-12=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B7x-12%3D0)
Solving the quadratic equation, we get,
i.e. x = -8.4 and x= 1.4
Since, the value of x cannot be negative.
Thus, x = 1.4 feet.