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Question
Math
Posted 6 months ago

The rectangle below has an area of 55x6+22x455 x^{6}+22 x^{4}.
The width of the rectangle is equal to the greatest common monomial factor of 55x655 x^{6} and 22x422 x^{4}.

What is the length and width of the rectangle?

Width == \square
Length == \square
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Answer from Sia
Posted 6 months ago
Solution by Steps
step 1
Find the greatest common divisor (GCD) of the monomials 55x655x^6 and 22x422x^4
step 2
The GCD of 55x655x^6 and 22x422x^4 is 11x411x^4
step 3
Divide the area of the rectangle 55x6+22x455x^6 + 22x^4 by the width 11x411x^4 to find the length
step 4
The length of the rectangle is 55x6+22x411x4=5x2+2\frac{55x^6 + 22x^4}{11x^4} = 5x^2 + 2
[question 1] Answer
Width =11x4= 11x^4
Length =5x2+2= 5x^2 + 2
Key Concept
Finding the dimensions of a rectangle given its area and width
Explanation
The width of the rectangle is the GCD of the monomial terms. The length is found by dividing the area by the width.

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