The length and width of the given rectangle will be 3m and 5m respectively.
Let us take width = a
So, the length will be = 2a-7
The area of a rectangle is the product of length and width.
So, the area of the rectangle will be length*width i.e. a(2a-7).
It is given that
a(2a-7) = 15
[tex]2a^2-7a =15\\\\2a^2-7a-15 = 0\\\\2a^2-10a+3a-15 = 0\\\\2a(a-5)+3(a-5)=0[/tex]
[tex](a-5) (2a+3)=0[/tex]
[tex]a=5\\a =-3/2[/tex]
"a" cannot take a negative value so a=5
So the width of the rectangle = 5m
Length of the rectangle = 2*5-7 = 3
Therefore, The length and width of the given rectangle will be 3m and 5m respectively.
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