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# Maths Help: Scale factor and quadratic? watch

1. Any help will be appreciated!

A rectangular playground of width x metres and length 3x metres is to be extended by adding 10 metres to its width to and 20 metres its length to form a larger rectangular playground. The area of the larger rectangular playground is double the area of the original playground.

a.) 3xsquared -50x -200=0
b.) calculate the area of the original playground.

I know it is to do with scale factors, and as a result have written area scale factor= scale factor squared
so the scale factor is actually 4?

I've drew the diagram, but haven't found it useful...
2. You shouldn't need scale factors - try finding an expression for the initial area and one for the final area of the playground. Then you can let twice the initial area equal the final area, and solve.
3. The only thing that I can see a scale factor is involved in is comparing the area of the original playground and the area of the new playground.

So you know that multiplying the area of the original playground by 2 gives you the area of the new playground, which resembles the equation in a). (You have to find the area of each playground before this step, in terms of x)

Solving part a) will help, but you should try and get to that equation first to understand how to do part b.
4. So:
(x+10)(3x+20) since the width was added by 10 and the length added 20. This is the area of the large playground
so (x+10)(3x+20)=2(x)(3x) since the large playground is 2 times the area of the smaller playground
Solve for x and substitute into the smaller playground figures to work that out

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Updated: January 21, 2015
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