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?

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DavidShotterid DavidShotterid · 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

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Limosaid Limosaid · Answer 2

Answer:

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

Step-by-step explanation:

Lets take the original length of a side of the Map is [tex]x[/tex] inches.

So the length of a side if the new Map = [tex]x+6[/tex] inches.

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

[tex]121=(x+6)^{2}[/tex]

[tex]\sqrt{121} =\sqrt{(x+6)^{2} }[/tex]

So, either

[tex]11=x+6[/tex] or [tex]-11=x+6[/tex]

[tex]5=x[/tex] or [tex]-17=x[/tex]

[tex]x[/tex] 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.