Answer:
The length is 12 cm and width is 6 cm
Step-by-step explanation:
The given are the area of the rectangle of 72[tex]cm^{2}[/tex] and the relation of its length and width.
Step 1: Identify the mathematical equation of the length and width of the given triangle. The problem states that length of the rectangle is twice its width which is equivalent to:
Length = 2 x width or L = 2w
Step 2: We know that the area of a rectangle is length multiplied by its width.
[tex]Area_{rectangle}[/tex] = L x W
Substitute the given relation of L and W, resulting to:
[tex]Area_{rectangle}[/tex] = 2w x w = 2[tex]w^{2}[/tex]
72[tex]cm^{2}[/tex] = 2[tex]w^{2}[/tex]
Step 3: Divide both sides by 2 and take the square root of both sides.
[tex]\frac{72 cm^{2} }{2}[/tex] = [tex]\frac{2 w^{2} }{2}[/tex]
[tex]\sqrt{36} cm^{2}[/tex] = [tex]\sqrt{w^{2} }[/tex]
w = 6 cm
Step 4: Substitute the resulting value of the rectangle's width to its relationship with the length.
L = 2w = 2 x 6 cm = 12 cm
Therefore, the length of the rectangle is 12 cm and the width is 6 cm.
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