I am really not sure if this is the right place to post a question like this, but I'm absolute stuck on this question. I would appreciate an answer greatly.

A park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that one side is doubled in length and the other is decreased by three meters. The new rectangular garden will have an area that is $25\%$ more than the original square garden. Write an equation that could be used to determine the length of a side of the original square garden. Then determine the area, in square meters, of the new rectangular garden.

(As an aside, I've gotten up to the point of finding the equation. Mine was $1.25x^2=(2x)(x-3)$. Not sure if this is correct, just trying to specify where I get stuck.)

  • 3
    $\begingroup$ Looks good to me. You can now divide both sides by $x$ since it's not zero, leaving $1.25x = 2(x-3)$. Multiply out the new RHS and solve. $\endgroup$ – Ken Jun 15 '15 at 1:12

Obviously, you get the correct relation, here it can be proved
Let $a$ be the side of the square garden then the new rectangular garden will have the length $2a$ (i.e. double the original side $a$) & width $a-3$ (i.e. decreased by $3$m from $a$). Now condition we have $$\text{area of new rectangular garden}=1.25\times(\text{area of original square garden})$$ $$\implies (2a)(a-3)=1.25(a^2)$$ $$\implies 2a^2-6a=1.25a^2$$ $$\implies 0.75a^2-6a=0$$ $$\implies \frac{3}{4}a^2-6a=0$$ $$\implies \color{blue}{a^2-8a=0}$$ $$\implies a(a-8)=0 \implies a=0, 8$$ But length of original garden $a>0$ Hence, the length of the original square garden $a=8$m.

Now the dimensions of the new rectangular garden are length $2a=16$m & width $a-3=5$m Hence the area of rectangular garden $$=16\times 5=80 \space m^2$$


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