a To build a perfect square, we have to place half of the x-tiles along the vertical side and the other half along the horizontal side of the x^2-tile.
B
b To build a perfect square, we have to place half of the x-tiles along the vertical side and the other half along the horizontal side of the x^2-tile.
C
c To build a perfect square, we have to place half of the x-tiles along the vertical side and the other half along the horizontal side of the x^2-tile.
A
a 25 unit tiles
B
b 9 unit tiles
C
c 121 unit tiles
Practice makes perfect
a Examining the expression, we notice that we have one x^2-tile and ten x-tiles. To build our perfect square, we have to place half of the x-tiles along the vertical side of the x^2-tile and the remaining half along the horizontal side.
If we add some helplines, we can identify the missing unit tiles we need to fill up the entire square.
As we can see, we need to add 25 unit tiles to build a perfect square.
b Examining the expression, we notice that we have one x^2-tile and six - x-tiles. To build our perfect square, we have to place half of the - x-tiles along the vertical side of the x^2-tile and the other half along the horizontal side.
If we add some helplines, we can identify the unit tiles missing to fill up the entire square.
As we can see, we need to add 9 unit tiles to build a perfect square.
c Like in previous parts, we will place half of the x-tiles along the horizontal side of the x^2-tile and the other half along the vertical side.
If we add some helplines, we can identify the unit tiles missing to fill up the entire square.
We need to add 11* 11=121 unit tiles to build a perfect square.
