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roselyn3301
25.06.2019 •
Mathematics
The rectangle below has an area of 14x^4+6x^214x 4 +6x 2 square meters. the width of the rectangle (in meters) is equal to the greatest common monomial factor of 14x^414x 4 and 6x^26x 2 . what is the length and width of the rectangle?
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Ответ:
Width = 2x² , Length = 7x² + 3
Step-by-step explanation:
The area of the rectangle = 14x⁴ + 6x²
The width of the rectangle (in meters) is equal to the greatest common monomial factor of 14x⁴ and 6x²
Factors of 14: 1 * 2 * 7
Factors of 6: 1 * 2 * *3
∴ The greatest common monomial factor of 14 and 6 = 2
Factors of x⁴: x , x² , x³ , x⁴
Factors of x²: x , x²
∴ The greatest common factor of x⁴ and x² = x²
∴ Width = 2x²
∵ Area = length times the width
∴ Length = Area/Width
Length =![\frac{14x^{4}+6x^2 }{2x^2} =\frac{2x^2*(7x^2+3)}{2x^2} =7x^2+3](/tpl/images/0016/4499/e1e32.png)
Ответ: