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

Given: A rectangular field whose diagonal is 16 meter more than the shorter side. and longer side is 14 meter long than the shorter side.

To do: To fine the lengths of the sides of the given rectangular field.

Solution: Let us consider ABCD is the rectangular field as shown in the figure.

And let b is the shorter side of the given rectangular farm,

$\therefore$ length of the rectangular farm$=b+14$

And diagonal of the rectangular farm$=b+16$

In $\vartriangle$ABD, on using pythagoras theorem,

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

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

$\Rightarrow 256+b^{2} +32b=196+b^{2} +28b+b^{2}$

$\Rightarrow b^{2} -4b-60=0$

$\Rightarrow b^{2} -10b+6b-60=0$

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

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

If $\ b+6=0$

$\Rightarrow b=-6$

If $\ b-10=0$

$\Rightarrow b=10$

Since side of a rectangle can't be negative, therefore we reject the value, $b=-6$

$\therefore b=10$

Therefore shorter side of the rectangular farm$=10$ meter

Longer side of the rectangular farm$=10+14=24$ meter.

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Updated on: 10-Oct-2022

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