Question

Question 6
The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

Answer 1

Let the shorter side of the rectangle be x m.
Then, larger side of the rectangle = (x + 30) m
Now as given in question diagonal length is 60 more than the shorter side, we can apply pythagoras theorem
$\Rightarrow x^2+(x+30{)}^2=(x+60{)}^2$
$\Rightarrow x^2+x^2+900+60x=x^2+3600+120x$
$\Rightarrow x^2-60x-2700=0$
$\Rightarrow x^2-90x+30x-2700=0$
$\Rightarrow x(x-90)+30(x-90)$
$\Rightarrow (x-90)(x+30)=0$
$\Rightarrow x=90,-30$
However, side cannot be negative. Therefore, the length of the shorter side will be 90 m.
Hence, length of the larger side will be (90 + 30) m = 120 m.