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The difference in the area of a large square and the area of a small square is 56 cm 2. If the side of the small square is 5 cm, find the perimeter of the large square.
- a)25 cm
- b)36 cm
- c)20 cm
- d)81 cm
Correct answer is option 'B'. Can you explain this answer?
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The difference in the area of a large square and the area of a small s...
Given:
Difference in area of large and small square = 56 cm²
Side of small square = 5 cm
To find: Perimeter of large square
Solution:
Let the side of the large square be 'x' cm.
Area of small square = side² = 5² = 25 cm²
Area of large square = x²
Difference in area of large and small square = x² - 25 = 56
x² = 56 + 25 = 81
x = √81 = 9 cm
Perimeter of large square = 4 × side = 4 × 9 = 36 cm
Therefore, the correct option is (b) 36 cm.
Note: We can also solve this problem by using algebra. Let the side of the large square be 'x' cm. Then, we have:
x² - 5² = 56
x² = 81
x = 9 cm
Perimeter of large square = 4 × side = 4 × 9 = 36 cm.
Difference in area of large and small square = 56 cm²
Side of small square = 5 cm
To find: Perimeter of large square
Solution:
Let the side of the large square be 'x' cm.
Area of small square = side² = 5² = 25 cm²
Area of large square = x²
Difference in area of large and small square = x² - 25 = 56
x² = 56 + 25 = 81
x = √81 = 9 cm
Perimeter of large square = 4 × side = 4 × 9 = 36 cm
Therefore, the correct option is (b) 36 cm.
Note: We can also solve this problem by using algebra. Let the side of the large square be 'x' cm. Then, we have:
x² - 5² = 56
x² = 81
x = 9 cm
Perimeter of large square = 4 × side = 4 × 9 = 36 cm.
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