Question

The width of a field is 5m less than its length. If the area is 204 m^2, find the dimmensions of the fiel

Answer 1

★ Given :

Breadth = Length - 5

Area of field = 204 m²

★ To Find :

Length = ?

Breadth = ?

★ Solution :

Let the length be “l” m

Let breadth be “b” m

$\boxed{ \: b = l - 5} \:$

Now , using the Formula for area of a rectangle .

$\rm \: area_{rectangle} = length \times breadth$

$\rm\mapsto {204 \: {m}^{2} } = l \times b$

$\rm\mapsto {204 \: {m}^{2} } = l \times b$

$\rm\mapsto \: 204 \: {m}^{2} = l \times (l - 5)$

$\rm\mapsto \: 204 = {l}^{2} - 5l$

$\rm\mapsto \: {l}^{2} - 5l - 204 = 0$

$\rm\mapsto \: {l}^{2} + 12l - 17l - 204 = 0$

$\rm \mapsto \: l(l + 12) - 17(l + 12) = 0$

Here,

either

$\rm\ \: l - 17 = 0 \\ \boxed{ \rm \ l = 17 \: m}$

or

$\rm \: l + 12 = 0 \\ \rm\ \: l = - 12$

it's not possible , as length is never negative .

so ,

$\boxed{\rm \: length \: = 17 \: m}$

and

$\rm \: breadth \: = 17 - 5 \: m$

$\boxed{\rm \: breadth \: = 12 \: m}$