Given that,
Length of a rectangular courtyard = (3x+5)
Width of a rectangular courtyard = (2x-3)
To find,
The expression for area of the courtyard.
Solution,
The area of the rectangular shaped object is given by :
A = lb
Substituting all the values,
A = (3x+5) (2-3)
= (3x)(2)-(3x)(3)+(5)(2)-(5)(3)
= 6x-9x+10-15
= -3x-5
So, the area of the courtyard is (-3x-5).
By direct calculation (multiplying the two given linear polynomials) we will see that the expression that represents the area is:
A = 6x^2 + x - 15
We know that the area of a rectangle of width W and length L is given by:
A = W*L
Here we know that:
L = 3x + 5
W = 2x - 3
Now we can just replace these in the area equation to get:
A = (3x + 5)*(2x - 3) = 6x^2 + 10x - 9x - 15
A = 6x^2 + x - 15
This is the expression that represents the area of the courtyard.
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