Question

Math

Posted 3 months ago

```
The rectangle below has an area of $55 x^{6}+22 x^{4}$.
The width of the rectangle is equal to the greatest common monomial factor of $55 x^{6}$ and $22 x^{4}$.
What is the length and width of the rectangle?
Width $=$ $\square$
Length $=$ $\square$
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

Find the greatest common divisor (GCD) of the monomials $55x^6$ and $22x^4$

step 2

The GCD of $55x^6$ and $22x^4$ is $11x^4$

step 3

Divide the area of the rectangle $55x^6 + 22x^4$ by the width $11x^4$ to find the length

step 4

The length of the rectangle is $\frac{55x^6 + 22x^4}{11x^4} = 5x^2 + 2$

[question 1] Answer

Width $= 11x^4$

Length $= 5x^2 + 2$

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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