width = 5.5 feet and
length = 8 feet
Step-by-step explanation:
Given:
Let Width = w
then length = 2.5 + w
Area = 44.8 square feet
Required:
Find length and Width
Formula:
[tex]Area = Length * Width[/tex]
Putting values to find length and width
[tex]Area = Length * Width\\44.8=(2.5+w)*w\\44.8=2.5w+w^2\\w^2+2.5w-44.8=0\\Solving\,\,using\,\,quadratic\,\,formula:\\w=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\w=\frac{-(2.5)\pm\sqrt{(2.5)^2-4(1)(-44.8)}}{2(1)}\\w=\frac{-2.5\pm\sqrt{6.25+179.2}}{2}\\w=\frac{-2.5\pm\sqrt{185.45}}{2}\\w=\frac{-2.5\pm13.618}{2}\\w=\frac{-2.5+13.618}{2}\,\,and\,\,w=\frac{-2.5-13.618}{2}\\w=5.5\,\,and\,\,w=-8.1[/tex]
So, value of w = 5.5 and -8.1
Since width can't be negative so,
Width = w = 5.5
Length = 2.5+w = 2.5+5.5 = 8
So, width = 5.5 feet and
length = 8 feet
Keywords: Area of rectangle
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