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shusha [124]
4 years ago
5

Can someone help me find the width and the length

Mathematics
1 answer:
ycow [4]4 years ago
5 0

Width of the rectangle = 5k^2

Length of the rectangle = 3 k^{2}+7 k+4

Solution:

Area of the rectangle = 15 k^{4}+35 k^{3}+20 k^{2}

Width of the rectangle = greatest common factor of 15 k^{4}, 35 k^{3}, \text { and } 20 k^{2}

Factor of 15k^4 = 5\times3\times k^2 \times k^2

Factor of 35k^3 = 5\times7\times k^2 \times k

Factor of 20k^2 = 5\times4\times k^2

Greatest common factor of 15 k^{4}, 35 k^{3}, \text { and } 20 k^{2}

                       = 5\times k^2

                       =5k^2

Width of the rectangle =5k^2

Area of the rectangle = length × width

15 k^{4}+35 k^{3}+20 k^{2}=\text{length}\times 5k^2

Divide by 5k² on  both sides.

$\frac{15 k^{4}+35 k^{3}+20 k^{2}}{5k^2} =\frac{\text{length}\times 5k^2}{5k^2}

$\frac{5k^2(3 k^{2}+7 k+4 )}{5k^2} =\text{length}

Cancel the common factor 5k², we get

3 k^{2}+7 k+4 =\text{length}

Switch the sides.

Length = 3 k^{2}+7 k+4

Width of the rectangle = 5k^2

Length of the rectangle = 3 k^{2}+7 k+4

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