Question

If the area of one small square box is 1 sq units and the area of the square on the side of AC is 225 sq units, then which of the following statements is correct?

• A. Area of the square along AC = Area of the square along BC - Area of the square along AC
• B. Area of the square along AB = Area of the square along BC + Area of the square along AC
• C. Area of the square along AC = Area of the square along AB + Area of the square along BC
• D. Area of the square along BC = Area of the square along AC + Area of the square along AB

Answer 1

The correct option is C Area of the square along AC = Area of the square along AB + Area of the square along BC

Area of the square on the side of AC = 225 sq units
The area of the above figure is 225 sq units. The number of small squares along the sides are 15.
And, since $225={15}^2$:
$\Rightarrow$ Area of the big square = (Number of small squares along the sides${)}^2$

If we count the number of small squares along the side AB, we will get 12 units.
$\Rightarrow$ Area of the blue square $={12}^2=144\text{sq units}$
(Area of the big square = (Number of small squares along the sides ${)}^2)$
If we count the number of small squares along the side BC, we will get 9 units.
$\Rightarrow$ Area of the pink square $=9^2=81\text{sq units}$
(Area of the big square = (Number of small squares along the sides ${)}^2)$
Now,
$225>144>81$ (Arranging the squares in descending order)
$225=144+81$ (Analyzing the squares of the sides)
Or
${15}^2={12}^2+9^2$
$\Rightarrow$ Area of the square along AC = Area of the square along AB + Area of the square along BC
$\to$ Option B is correct.