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.

Step-by-step 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 (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