# Thread: rectangle with unknown sides?

1. ## rectangle with unknown sides?

Ok we have this rectangle questiosn that makes no sense to me.

Here is a diagram of the question

The smaller rectangle is 4 by 5 metres which the area would be 20 metres. Then the rectangle 'grows' bigger and then has an area of 56mē. How do I get the length and the width of the second rectangle? I think I know the answer but I don't know how to get it.

Any help is greatly appriciated, thanks!

2. Originally Posted by risteek
Ok we have this rectangle questiosn that makes no sense to me.

Here is a diagram of the question

The smaller rectangle is 4 by 5 metres which the area would be 20 metres. Then the rectangle 'grows' bigger and then has an area of 56mē. How do I get the length and the width of the second rectangle? I think I know the answer but I don't know how to get it.

Any help is greatly appriciated, thanks!
Let's assume that the sides increse by a constant factor k. (The question doesn't state that the ratio of length to width is a constant!)

Then you know about the new length L = 5k and the new width W = 4k and therefore

$5k \cdot 4k = 56~\implies~ 20k^2 = 56~\implies~ k^2 = 2.8$

and therefore the dimensions of the new rectangle are:

$(5 \cdot \sqrt{2.8}) \cdot (4 \cdot \sqrt{2.8})=56$

3. Thank you for your help! It means a lot! =)