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

If she wants the area to be double, then we need to find the current area.\[3\times4=12\]So, double that is obviously 24. If she wants to increase the sides by the same length, and still have double the area, then she needs to increase the sides by about 1.4 feet. \[4.4\times5.4=23.76\]

Answer 2

Hmm lets write some equations...

Length = 3
Width = 4

Area = 3 x 4 = 12 <--area of the original

Area of the wanted has to be twice that...so 24

We know Area = L x W...

So L x W = 24

The new length will be the old length + some amount...and the width will be the old + that same amount...so we have

(L + x) x (W + x) = 24

We know the original length and width

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

Distribute

x^2 + 7x + 12 = 24

Solve for the zeros of the equation

\[\large x^2 + 7x + 12 = 24\]
\[\large x^2 + 7x = 12\]
\[\large x^2 + 7x + 12.25 = 24.25\]
\[\large (x + 3.5)^2 = 24.25\]
\[\large x + 3.5 = \pm \sqrt{24.25}\]
\[\large x = -3.5 \pm \sqrt{24.25}\]
\[\large x = 1.4, \cancel{8.4}\]