Question

Francine has a picture whose length is its width. She wants to enlarge the picture to have an area of 192 in2. What will the dimensions of the enlarged picture be? Model the scenario and solve. Then, explain in at least one sentence your solution and include the reasonableness of your solution.

Answer 1

1. The measures of the length and the width of the picture are equal, so the picture is square shaped.

2. The enlarged picture will still be a square, since when we enlarge, we enlarge all distances with the same factor.

3. Let the dimensions of the large picture be a (length) by a (width)

4. Area of picture = $a^{2}=192 in^{2}$

$a= \sqrt{192} = \sqrt{16*12}= \sqrt{16*4*3}=4*2* \sqrt{3}=8\sqrt{3} (feet)$

Answer: the dimensions are $8\sqrt{3} (feet)$ by $8\sqrt{3} (feet)$