Question

A rectangular field has a length $10$ units more than it is width. If the area of the field is $264$, what are the dimensions of the rectangular field?

Answer 1

As we know that the formula of area of a rectangle with dimensions of length $x$ and breadth $y$ is $=$ $x\times y$
Hence $264$ $=$ $x\times y$
As per the given information the value of $x$ is $y+10$ and hence we get the equation as,
$264=y\times (y+10)$
$264=y^2+10y$
or $y^2+10y-264=0$
By factorizing this trinomial we get the factors as,
$(y-12)(y+22)=0$
To make this true we have to take the value of $x$ such that the value of $x$ is positive ( because neither the length nor the breadth can be in negative) . Here we are left with just one option of taking the value of $x$ in the first factor as $12$.
Now as we have the dimension of the breadth $=$ $12$ units
The dimension of the length will be $=$ $12+10=22$ units.