Question

The diagonal of a rectangular field is 16 m more than the shorter side. If the longer side is 14 m more than the shorter side, then find the lengths of the sides of the field.

Answer 1

Let $l$ be the length of the longer side and $b$ the length of the shorter side.

Given that the length of the diagonal of the rectangular field is 16 m and more than shorter side.

Thus, Diagonal =$16+b$

Since the longer side is 14 more than shorter side, $l=14+b$
We know,

$(\text{Diagonal}{)}^2=(\text{Length}{)}^2+(\text{Breadth}{)}^2$

[By Pythagoras therorem]

$\therefore (16+b{)}^2=(14+b{)}^2+b^2$

$256+b^2+32b=196+b^2+28b+b^2$

$b^2-4b-60=0$

$b^2-10b+6b-60=0$

$(b-10)+6(b-10)=0$

$(b+6)(b-10)=0$

$\Rightarrow b=-6or+10$

As breadth cannot be negative

$\therefore Breadth\left(b\right)=10m$

Now,length of rectangular field=(14+b) m

=(14+10)m

=24 m

Thus,length of rectangular field is 24 cm and breadth is 10 m.