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.

Answer 1

B. 1.4 feet

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,
`A_(c)` = length × breadth = 4 × 3 = 12 ft²

Since, the area of display model is twice the area of the canvas. We have,

`A_(d)` = 2 ×
`A_(c)`

i.e.
`A_(d)` = 2 × 12

i.e.
`A_(d)` = 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,

`A_(c)` = length × breadth = (x+4) × (x+3) =
`x^(2) +7x+12`

Since,
`A_(d)` = 24 ft²

i.e.
`x^(2) +7x+12` = 24

i.e.
`x^(2) +7x-12=0`

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.