Answer:
length is 7 inches and the width is 5 inches
Step-by-step explanation:
Hello, I think I can help you with this
the area of a rectangle is given by:
![(equation1)Area=length * width\\](https://tex.z-dn.net/?f=%28equation1%29Area%3Dlength%20%2A%20width%5C%5C)
Step 1
According to the question data,the length is two inches longer than its width.which means that you can take the width and add 2 inches to obtain the length, in mathematical terms
(equation 2)Width + 2 inches = length
Step 2
Now, put equation 2 into equation 1
![Area=length * width\\Area=(width + 2 )*width\\Area=width^{2}+2widht\\Let\ width=w](https://tex.z-dn.net/?f=Area%3Dlength%20%2A%20width%5C%5CArea%3D%28width%20%2B%202%20%29%2Awidth%5C%5CArea%3Dwidth%5E%7B2%7D%2B2widht%5C%5CLet%5C%20width%3Dw)
Step 3
replace and solve for w
Let
A=35
![A=35\\Area=w^{2} +2w\\35=w^{2} +2w\\w^{2} +2w-35=0\\use\ quadratic\ formula\ to\ solve\\if\\ax^{2} +bx+c=0\\x=\frac{-b +- \sqrt[2]{b^{2}4ac } }{2a}\\ +- means\ there\ are\ 2\ solutions, we\ will\ take\ the\ positive\ one, because\ it\ is\ a\ distance.\\Now, replacing\\a=1,b=2,c=35\\\\w=\frac{-2 + \sqrt[2]{2^{2}-4*1*-35 } }{2*1}\\w=\frac{-2 + \sqrt[2]{4+140} }{2}\\w=\frac{-2+\sqrt{144} }{2} \\w=\frac{-2+12}{2}\\w=\frac{10}{2}\\w=5](https://tex.z-dn.net/?f=A%3D35%5C%5CArea%3Dw%5E%7B2%7D%20%2B2w%5C%5C35%3Dw%5E%7B2%7D%20%2B2w%5C%5Cw%5E%7B2%7D%20%2B2w-35%3D0%5C%5Cuse%5C%20quadratic%5C%20formula%5C%20to%5C%20solve%5C%5Cif%5C%5Cax%5E%7B2%7D%20%2Bbx%2Bc%3D0%5C%5Cx%3D%5Cfrac%7B-b%20%2B-%20%5Csqrt%5B2%5D%7Bb%5E%7B2%7D4ac%20%7D%20%7D%7B2a%7D%5C%5C%20%2B-%20means%5C%20there%5C%20are%5C%202%5C%20solutions%2C%20we%5C%20will%5C%20take%5C%20the%5C%20positive%5C%20one%2C%20because%5C%20it%5C%20is%5C%20a%5C%20distance.%5C%5CNow%2C%20replacing%5C%5Ca%3D1%2Cb%3D2%2Cc%3D35%5C%5C%5C%5Cw%3D%5Cfrac%7B-2%20%2B%20%5Csqrt%5B2%5D%7B2%5E%7B2%7D-4%2A1%2A-35%20%7D%20%20%7D%7B2%2A1%7D%5C%5Cw%3D%5Cfrac%7B-2%20%2B%20%5Csqrt%5B2%5D%7B4%2B140%7D%20%20%7D%7B2%7D%5C%5Cw%3D%5Cfrac%7B-2%2B%5Csqrt%7B144%7D%20%7D%7B2%7D%20%5C%5Cw%3D%5Cfrac%7B-2%2B12%7D%7B2%7D%5C%5Cw%3D%5Cfrac%7B10%7D%7B2%7D%5C%5Cw%3D5)
so, the width is 5 inches,
replacing this value in equation 2
Width + 2 inches = length
5 in +2 in =length
7 in = length
so , the length is 7 inches
Have a good day.