Question

Jonas has a puzzle as shown. The two square pieces cover an area of $1000c{m}^2$. The side of the smaller square is $xcm$, and the side of the bigger square is $x+10cm$. The outline of the whole puzzle is also a square. What is the combined area of the rectangular missing pieces?

• A. $450c{m}^2$
• B. $900c{m}^2$
• C. $225c{m}^2$
• D. $1350c{m}^2$

Answer 1

The correct option is B $900c{m}^2$


The side of the smaller square is $x$; the side of the bigger square is $x+10$.

Area of two squares $=x^2+(x+10{)}^2=1000c{m}^2$
$⟹2x^2+20x+100=1000$
$⟹x(x+10)=450$ …(i)

The dimensions of each of the rectangle are $x$ and $x+10$.

Area of one of the shaded rectangles $=x(x+10)$
This can be obtained from (i).
$⟹x(x+10)=450c{m}^2$

Total area of the missing pieces $=2\times 450=900c{m}^2$