The length is 15 inches and width is 9 inches
Step-by-step explanation:
Let
l be the length
and
w be the width
w = l-6
The area of rectangle is 135 ft^2
The formula for area is:
![Area=l*w\\135=l*(l-6)\\135=l^2-6l\\l^2-6l-135=0\\l^2+9l-15l-135=0\\l(l+9)-15(l+9)=0\\(l+9)(l-15)=0\\l+9 = 0 => l=-9\\l-15 = 0 => l=15\\](https://tex.z-dn.net/?f=Area%3Dl%2Aw%5C%5C135%3Dl%2A%28l-6%29%5C%5C135%3Dl%5E2-6l%5C%5Cl%5E2-6l-135%3D0%5C%5Cl%5E2%2B9l-15l-135%3D0%5C%5Cl%28l%2B9%29-15%28l%2B9%29%3D0%5C%5C%28l%2B9%29%28l-15%29%3D0%5C%5Cl%2B9%20%3D%200%20%3D%3E%20l%3D-9%5C%5Cl-15%20%3D%200%20%3D%3E%20l%3D15%5C%5C)
As the length cannot be negative, so we will use the value of length 15
If length 15,
w=l-6
w=15-6
w=9
So,
The length is 15 inches and width is 9 inches
Keywords: Area of rectangle, Quadratic equation
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