Answer:
Length = [tex]\frac{189}{4}\ m[/tex]
Width = 21 m
Area of garden = 992.25 [tex]m^{2}[/tex]
Step-by-step explanation:
Side of square = 1 cm
As per the given question figure, we can see that there are 11 square across the length of rectangular garden.
But the garden includes only 9 squares, the corner squares are not in the garden.
So, length of garden = 9 [tex]\times[/tex] 1 = 9 cm
Using the scaling given in the question,
[tex]\dfrac{2}{3}\ cm = 3\dfrac{1}{2}\ m\\[/tex][tex]\Rightarrow \dfrac{2}{3}\ cm = \dfrac{7}{2}\ m[/tex]
[tex]1 cm = \dfrac{\dfrac{7}{2}}{\dfrac{2}{3}} \ m \Rightarrow \dfrac{21}{4}\ m[/tex]
So, length of garden = [tex]\dfrac{21}{4} \times 9 \Rightarrow \dfrac{189}{4}\ m[/tex]
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And, similarly width contains 4 squares, (Corner squares are excluded)
Width of garden = [tex]\dfrac{21}{4} \times 4 \Rightarrow 21\ m[/tex]
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Area of garden = Length [tex]\times[/tex] Width
[tex]\Rightarrow \dfrac{189}{4} \times 21\\\Rightarrow \dfrac{3969}{4}\\\Rightarrow 992.25\ m^{2}[/tex]
