SOLUTION: The length of a rectangle is 7 meters more than the width. the length of a diagonal is 13 meters. find the length

You can put this solution on YOUR website!
Although the problem gives you the information as if you were looking for the sides of a rectangle, the fact that it gives you the length of the diagonal means that you can treat the information as if it were about a right triangle. We can use the Pythagoream theorem:
a² + b² = c²

However, we only know definitively the length of the diagonal. In order to solve a single equation, we can only have one variable.
width: w
length of the rectangle: w + 7
diagonal: 13

Now we can set up the equation:
w² + (w+7)² = 13²
w² + w² + 14w + 49 = 169
2w² + 14w - 120 = 0
w² + 7 w - 60 = 0
(w+12)(w-5) = 0


There are two options. Either w+12 = 0 or w-5=0. However, only one of these will have a positive numbered answer.
w + 12 = 0
w = -12
This is wrong because the width can't be negative.

w-5 = 0
w = 5
This must be the width.

Now we can find the length of the rectangle:
length = w + 7
= 5 + 7
= 12

Therefore, for this rectangle, the width is 5 meters and the length is 12 meters.