Question

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

Answer 1

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★ The width of the field is 5m less than it's length . If the area is 204 m² , find the dimensions of the field .

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★ 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 .

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

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

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

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

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

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

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

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

Here,

either

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

or

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

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

so ,

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

and

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

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

★ Know More :

• Area of rectangle = length × breadth
• Perimeter of rectangle = 2(length + breadth)
• the unit of area is always in square i.e. (unit)²
• The unit of Perimeter is units , it can be cm , m , km etc .