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

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:

$(equation1)Area=length * width$

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

$A=35\\Area=w^{2} +2w\\35=w^{2} +2w\\w^{2} +2w-35=0\\use\ quadratic\ formula\ to\ solve\\if\\ax^{2} +bx+c=0\\x=\frac{-b +- \sqrt[2]{b^{2}4ac } }{2a}\\ +- means\ there\ are\ 2\ solutions, we\ will\ take\ the\ positive\ one, because\ it\ is\ a\ distance.\\Now, replacing\\a=1,b=2,c=35\\\\w=\frac{-2 + \sqrt[2]{2^{2}-4*1*-35 }  }{2*1}\\w=\frac{-2 + \sqrt[2]{4+140}  }{2}\\w=\frac{-2+\sqrt{144} }{2} \\w=\frac{-2+12}{2}\\w=\frac{10}{2}\\w=5$

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.