Question

Francine has a picture whose length is twice its width. She wants to enlarge the picture to have an area of 242 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

Since it is not possible to have a negative width, the solution “-11” is ignored.

The width must be 11 and the height would then be twice that amount: h=2(11)=22

Explanation:

used this on my test and it was correct.

Answer 2

Explanation:

She wants to enlarge the picture to have an area of 242 in².

Suppose the width of the enlarged picture be "X".

then the length of the enlarged picture would be 2X.

The area of the enlarged picture would be (length times width).

2X * X = 242 in²

2X² = 242

x² = 242/2 = 121

x = 11 inches

So, width of the enlarged picture = 11 inches.

and, length of the enlarged picture = 22 inches.

When we enlarge the picture, its shape does not change, only the size changes and everything remains in same ratio. If the original picture has its length as twice as its width, then the enlarged picture would be in same proportion.

So it is quite reasonable that the length of enlarged picture would be as twice as its width. Hence the dimensions of enlarged picture are 11 in x 22 in.