Question 151724
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:
a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup>
<br>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
<br>Now we can set up the equation:
w<sup>2</sup> + (w+7)<sup>2</sup> = 13<sup>2</sup>
w<sup>2</sup> + w<sup>2</sup> + 14w + 49 = 169
2w<sup>2</sup> + 14w - 120 = 0
w<sup>2</sup> + 7 w - 60 = 0
(w+12)(w-5) = 0
<br>
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.
<br>w-5 = 0
w = 5
This must be the width.
<br>Now we can find the length of the rectangle:
length = w + 7
= 5 + 7
= 12
<br>Therefore, for this rectangle, the width is 5 meters and the length is 12 meters.