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If the length of a side of a square increased by 8 cm, its area increased by 120 square cm. What is the length of a side of the square?
  • a)
    2.5 cm
  • b)
    3.5 cm
  • c)
    4.5 cm
  • d)
    5.5 cm
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If the length of a side of a square increased by 8 cm, its area increa...
Let the original length of the side of the square be x cm
Area = side2
If the length increases by 8cm, area increased by 120 cm2
(x + 8)2 - x2 = 120
x2 + 16x + 64 - x2 = 120 [∵ (a + b)2 = a2 + 2ab + b2]
16x = 56
∴ x = 3.5 cm
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Most Upvoted Answer
If the length of a side of a square increased by 8 cm, its area increa...

Given Information:
- Increase in the side length of the square: 8 cm
- Increase in the area of the square: 120 square cm

Solution:
Let the original side length of the square be x cm.

Original Area:
Area = side length x side length
Original Area = x cm x x cm = x^2 square cm

Increased Area:
New side length = x + 8 cm
New Area = (x + 8) cm x (x + 8) cm = (x^2 + 16x + 64) square cm

Given Information:
New Area - Original Area = 120 square cm
(x^2 + 16x + 64) - x^2 = 120
16x + 64 = 120
16x = 56
x = 3.5 cm

Therefore, the length of a side of the square is 3.5 cm, which corresponds to option B.
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If the length of a side of a square increased by 8 cm, its area increased by 120 square cm. What is the length of a side of the square?a)2.5 cmb)3.5 cmc)4.5 cmd)5.5 cmCorrect answer is option 'B'. Can you explain this answer?
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