Answer:
[tex]\fbox{length= 10 \: in}
[/tex]
Step-by-step explanation:
Given:
Length to Width Ratio = 2:3
Area of Rectangle= 150 in²
To find:
Length of rectangle=?
Solution:
Assume the length of rectangle is 2x
and the width of rectangle is 3x
Now,
we know that,
[tex]\sf\: Area \: of \: Rectangle = Length \times Width \\ \sf \: 150 = 2x \: \times 3x \\ \sf \: 150 =6 {x}^{2} \\ \sf \: {x}^{2} = \frac{150}{6} \\ \sf {x}^{2} = \cancel\frac{150}{6} \\\sf {x}^{2} = 25 \\\sf \sqrt{ {x}^{2} } = \sqrt{ {25} } \\ \sf \sqrt{ {x}^{2} } = \sqrt{ {5}^{2} } \\ \sf \: \fbox{x = 5 \: in}[/tex]
Substituting the value of x in assumption,
[tex] \sf \: length= 2x \\ \sf \: length= 2 \times 5 \\ \sf \: \fbox{length= 10 \: in}
[/tex]
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