The largest dimension of the enlarged photo will be: Width= 175 inches and Length= 245 inches.
<u><em>Explanation</em></u>
Dimension of the original photo is 5×7 . That means the ratio of the width to the length is 5 : 7
So, lets assume the width is
and length is
for the enlarged photo.
Formula for the perimeter of a rectangle ![=2(length+width)](https://tex.z-dn.net/?f=%3D2%28length%2Bwidth%29)
As the perimeter of the enlarged photo should not exceed 840 inches, so...
![2(7x+5x)\leq 840\\ \\ 2(12x)\leq 840\\ \\ 24x\leq 840\\ \\ x\leq \frac{840}{24}\\ \\ x\leq 35](https://tex.z-dn.net/?f=2%287x%2B5x%29%5Cleq%20840%5C%5C%20%5C%5C%202%2812x%29%5Cleq%20840%5C%5C%20%5C%5C%2024x%5Cleq%20840%5C%5C%20%5C%5C%20x%5Cleq%20%5Cfrac%7B840%7D%7B24%7D%5C%5C%20%5C%5C%20x%5Cleq%2035)
That means the maximum value of
must be 35.
So, the largest possible width
inches
and the largest possible length
inches