Question 151724: The length of a rectangle is 7 meters more than the width. the length of a diagonal is 13 meters. find the length
Answer by mducky2(62)   (Show Source):
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.
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