Question

The area of a photograph is 35 square inches. Its length is two inches longer than its width. Find the length and width of

the photograph

Answer 1

length is 7 inches and the width is 5 inches

Explanation:

Hello, I think I can help you with this

the area of a rectangle is given by:

`(equation1)Area=length * width\\`

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`

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=(-2+√(144) )/(2) \\w=(-2+12)/(2)\\w=(10)/(2)\\w=5`

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.