The area of a square is three-fifths the area of a rectangle. The length of the rectangle is 25 cm and its breadth is 10 cm less than its length. What is the perimeter of the square?

### Concept & Formulas This problem requires calculating the area of a rectangle to find the area of a related square, and then extracting the square's perimeter. $$ \text{Area of Rectangle} = \text{length} \times \text{breadth} $$ $$ \text{Area of Square} = \frac{3}{5} \times \text{Area of Rectangle} $$ ### Step-by-Step Solution - **Given**: Length of rectangle ($L$) $= 25$ cm. Breadth ($B$) is $10$ cm less than length. - Calculate Breadth: $B = 25 - 10 = 15$ cm. - Calculate Rectangle Area: $25 \times 15 = 375$ sq. cm. - Calculate Square Area: $\frac{3}{5} \times 375$. - Simplify: $3 \times (375 / 5) = 3 \times 75 = 225$ sq. cm. - Let the side of the square be $a$. So, $a^2 = 225 \implies a = 15$ cm. - Calculate Square Perimeter: $4 \times a = 4 \times 15 = 60$ cm. ### Exam Strategy & Shortcut You can cancel factors early to save calculation time. Square Area $= \frac{3}{5} \times (25 \times 15) = 3 \times 5 \times 15 = 225$. Then recognize $225$ as $15^2$, making the perimeter $4 \times 15 = 60$. ### Common Pitfall Stopping at the side length ($15$) or the area ($225$) and looking for those in the options instead of completing the final step to find the perimeter. ### Final Answer Therefore, the correct answer is **60 cm**.