Question

Joaquin has created a small treasure map that is in the shape of a square. He decides to make a larger version of the map, and on this new map he increases each side by 6 inches. The area of this larger version of the map is 121 square inches. What are the dimensions of his original, smaller map?

Answer 1

(l+6)(l+6)=121=l^2+6l+6l+36
l^2+12l-85=(l-5)(l+17)
l=5 or l =-17
cannot be negative
therefore was a 5 by 5 map

Answer 2

The length of a side of the smaller map is 5 inches.

Explanation:

Lets take the original length of a side of the Map is
`x` inches.

So the length of a side if the new Map =
`x+6` inches.

Area of a square = (Length of a side)²

`121=(x+6)^(2)`

`√(121) =\sqrt{(x+6)^(2)  }`

So, either

`11=x+6` or
`-11=x+6`

`5=x` or
`-17=x`

`x` cannot be a negative value as it is a length of a square.

Therefore. the length of a side of the smaller map is 5 inches.