how do you solve this?

The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let [tex]x[/tex] represent the width.

Since the length is 7 feet longer, we can represent the length by [tex]x+7[/tex].

Now that we have our values for the length and the width we can multiply them together to find our area.

[tex](x)(x+7)=x^{2} +7x[/tex]

Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.

[tex](x+7)(x+14)[/tex]

And multiply our area by 3.

[tex]3(x^{2} +7x)[/tex]

set these equal to each other to find your new equation.

[tex](x+7)(x+14)=3(x^{2} +7x)[/tex]

Now you need to solve for [tex]x[/tex]. To do this first muliply [tex](x+7)[/tex] and [tex](x+14)[/tex].

[tex](x+7)(x+14)=\\x^{2} +14x+7x+98=\\x^{2} +21x+98[/tex]

Then multiply [tex]3(x^{2} +7x)[/tex]

[tex]3(x^{2} +7x)=\\3x^{2} +21x[/tex]

Now you can begin solving for [tex]x[/tex].

[tex]x^{2} +21x+98=3x^{2} +21x[/tex]

Subtract [tex]x^{2}[/tex] from both sides.

[tex]21x+98=2x^{2} +21x[/tex]

Subtract [tex]21x[/tex] from both sides.

[tex]98=2x^{2}[/tex]

Divide by 2.

[tex]49=x^{2}[/tex]

And finally take the sqaure root of both sides.

[tex]\sqrt{x^{2} }=\sqrt{49}\\x=7[/tex]

Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 and -7, in this case we only get +7.

Now that we have the value of [tex]x[/tex], we can plug it into our original values.

For width we simply get 7.

For length we get 7+7=14

To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.