Two squares are drawn on a same base but of different edge length. If difference of their area is 36 sq.cm. find the edge length of larger square if difference of their edge length is 3 cm.

Options

A. A)5.5 cm
B. B)7.5 cm
C. C)6.5 cm
D. D)4.5 cm

Answer

To solve the problem step by step, we will denote the edge length of the larger square as \( a \) cm and the edge length of the smaller square as \( a - 3 \) cm (since the difference in their edge lengths is 3 cm).

### Step 1: Write the area of both squares
The area of the larger square is given by:
\[ \text{Area of larger square} = a^2 \]
The area of the smaller square is given by:
\[ \text{Area of smaller square} = (a - 3)^2 \]

### Step 2: Set up the equation for the difference in area
According to the problem, the difference in their areas is 36 sq. cm. Therefore, we can set up the equation:
\[ a^2 - (a - 3)^2 = 36 \]

### Step 3: Expand the equation
Now we need to expand \( (a - 3)^2 \):
\[ (a - 3)^2 = a^2 - 6a + 9 \]
Substituting this back into the equation gives us:
\[ a^2 - (a^2 - 6a + 9) = 36 \]

### Step 4: Simplify the equation
Now simplify the left-hand side:
\[ a^2 - a^2 + 6a - 9 = 36 \]
This simplifies to:
\[ 6a - 9 = 36 \]

### Step 5: Solve for \( a \)
Now, add 9 to both sides:
\[ 6a = 36 + 9 \]
\[ 6a = 45 \]
Now, divide both sides by 6:
\[ a = \frac{45}{6} = 7.5 \text{ cm} \]

### Conclusion
The edge length of the larger square is \( 7.5 \) cm.