Question

Please help

Francine has a picture with a length its width. She wants to enlarge the picture to have an area of 375 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

correct

Explanation:

Answer 2

25 in x 15 in

Explanation:

Given:

• Length = 3/5 the width
• Area = 375 in²

Let width =
`x`

Therefore, length = 3/5
`x`

First create an equation for the area of the picture based on the given information for its width and length:

`\begin{aligned} \implies \textsf{Area of original picture} & = \sf width * length\\& = x\left((3)/(5)x\right)\\& = (3)/(5)x^2\end{aligned}`

We are told the area of the enlarged picture is 375 in². Therefore, substitute this into the equation and solve for
`x` to find the width of the enlarged picture:

`\begin{aligned}\textsf{Area} & = 375\\ \implies (3)/(5)x^2 & = 375\\ x^2 & =375 \cdot (5)/(3)\\ x^2 & =625\\ x & = √(625)\\ x& = 25\end{aligned}`

Therefore, the width of the enlarged picture is 25 in.

Substitute the found value of
`x` into the expression for length to find the length of the enlarged picture:

`\begin{aligned}\sf Length & = (3)/(5)x\\\\\implies \sf Length & = (3)/(5)(25)\\\\& = 15\: \sf in\end{aligned}`

Therefore, the dimensions of the enlarged picture are 25 in x 15 in. The width is 25 in and the length is 15 in, as the length is 3/5 of the width.