Question

Help me... with explanation plz...​

Answer 1

`w=3`

Explanation:

You can write a few equations for this situation.

This is a rectangle, and rectangles have right angles. That means that the given diagonal distance makes a right triangle with the length and width.

Solve for w using the pythagorean theorem:

`w^2+(w+2)^2=5.83^2\\w^2+w^2+4w+4=33.9889`

I'm pretty sure 33.9889 is actually 34, the reason it isn't is because 5.83 was rounded to only 2 decimal places, which doesn't accurately show represent what it's supposed to be. The problem also has you round to the nearest inch, so the answer wouldn't change. It just makes the calculations significantly easier.

`2w^2+4w+4=34\\2w^2+4w-30=0\\2(w^2+2w-15)=0\\2(w-3)(w+5)=0\\w=3,-5`

Distances can't be negative, so
`w=3`.