Answer:
Side length of first square is 10 cm
Side length of second square is 8 cm
Explanation:
Let (x + 2) = side length of first square
Let x = side length of second square
Area of a square = (side length)²
⇒ area of first square = (x + 2)²
⇒ area of second square = x²
If the sum of their areas is 100 cm² then:
⇒ (x + 2)² + x² = 100
Expand the brackets:
⇒ x² + 4x + 4 + x² = 100
Collect and combine like terms:
⇒ 2x² + 4x + 4 = 100
Subtract 100 from both sides:
⇒ 2x² + 4x - 96 = 0
Divide both sides by 2:
⇒ x² + 2x - 48 = 0
Factor:
⇒ (x - 6)(x + 8) = 0
Therefore,
⇒ x = 6, x = -8
As distance is positive, x = 8 only.
Therefore, side length of first square is 10 cm
Side length of second square is 8 cm