A square has side length 6x+2. A rectangle with width 3x+1 has the same area as a square. What is the length of the rectangle
2 answers:
Answer:
L = 12x + 4
Step-by-step explanation:
(see diagram for reference)
the area of the square
= (6x+2) (6x+2) (factor out 2 from each parentheses)
= (2)(3x+1)(2)(3x+1) (group like terms and simplify)
= 4(3x + 1)²
the area of the rectangle,
= (3x+1) (L)
It is given that the square and the circle have the same area, hence we equate the areas of square and rectangle:
4(3x + 1)² = (3x+1) (L) (divide both sides by 3x+1)
4(3x + 1) = (L) (rearranging and expanding the parentheses)
L = 12x + 4
Hope this helps
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