Someone please help me. Solve
Holly has a rectanglar garden that measures 12m by 14m. She wants to increase the area to 255m by increasing the width and length by the same amount. What will be the dimensions of the new garden?
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lets call the number we increase by \(x\) so we already have an area of \(12\times 14=168\) and we want to increase it to 255 so we need \((12+x)(14+x)=255\) and we have to solve for x
The current area is 12*14 = 168m square
Let 'x' be the dimension she increases the width and lengths by, the new dimensions will be
(12+x) and (14+x) and when you multiply these two, you should get 255
(12+x)(14+x) = 255
x^2 + 26x -87 = 0
Solve this quadratic equation and you get x= 3 and x=-29
Since length dimensions cannot be negative, we ignore -29 and follow up with x=3
The new dimensions of garden will be 15m by 17m
You can verify answer by calculating new area = (15*17) = 255m
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How did you get 15 and 17?
When we solved the quadratic equation, we got the values of x as 3 and -29. As I mentioned, we will ignore -29 and go with x=3
Our original dimensions were 12 by 14. 'x' is the increase in these dimensions, therefore the new dimensions will be 12+x and 14+x. Replacing x by 3 gives us 15 by 17. Does that clear things?