Question

a photographer wants to enlarge a 5x7 photo for a wall mural without distorting its width-to- length ratio. What are the largest dimensions to which he can enlarge the photo without having its perimeter exceed 840 inches?

Answer 1

The largest dimension of the enlarged photo will be: Width= 175 inches and Length= 245 inches.

Explanation

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 $5x$ and length is $7x$ for the enlarged photo.

Formula for the perimeter of a rectangle $=2(length+width)$

As the perimeter of the enlarged photo should not exceed 840 inches, so...

$2(7x+5x)\leq 840\\ \\ 2(12x)\leq 840\\ \\ 24x\leq 840\\ \\ x\leq \frac{840}{24}\\ \\ x\leq 35$

That means the maximum value of $x$ must be 35.

So, the largest possible width $=5x=5*35=175$ inches

and the largest possible length $= 7x= 7*35=245$ inches