I need help with the following question:
A playground, which measures 60m by 40m, is to be doubled in area by extending each side of the playground by an equal amount. Determine how much eash side should be extended.
the original area is 60*40 = 2400 cubic meters
Let the length each side is extended by be $\displaystyle x$.
Thus the new area is given by:
$\displaystyle A = (60 + x)(40 + x)$
we are told that with this extension, the area is doubled. thus we have,
$\displaystyle (60 + x)(40 + x) = 4800$
now solve for $\displaystyle x$ to find the extension
do you know how to expand brackets? take each term in one set of brackets and multiply each term in the other set
$\displaystyle (60 + x)(40 + x) = 4800$
$\displaystyle \Rightarrow 2400 + 60x + 40x + x^2 = 4800$
$\displaystyle \Rightarrow x^2 + 100x - 2400 = 0$
this is a quadratic equation, can you continue?