Question

maths leniear equation question ​

Answer 1

$\underline{ \underline{ \Large \bf { Given:} } }$

• Perimeter of the rectangular plot = 750 m

[ Since, it has fenced with a wire ; so the length of the wire is the plot's perimeter.]

• Length of the plot exceeds the breadth by 5 m.

$\underline{ \underline{ \Large \bf { To \: calculate:} } }$

• The length & breadth of the plot.

$\underline{ \underline{ \Large \bf { Calculation :} } }$

Let,

• Length = $\ell$
• Breadth = b

According to the question,

$\pmb {\rm {\mapsto \ell = b + 5} }$

[ As length exceeds the breadth by 5 m.]

So,

$\pmb {\rm {\mapsto b = \ell - 5. . . . . . . (i)} }$ (By transposition)

As we know that,

$\longmapsto \pmb {\rm \green { Perimeter_{(Rectangle)} = 2 (\ell + b )} }$

Substituting the value of breadth from the equation (i).

$\longmapsto \pmb {\rm { Perimeter_{(Rectangle)} = 2 (\ell + \ell - 5)} }$

$\longmapsto \pmb {\rm { 750 \: m = 2(2\ell - 5) \: m} }$

$\longmapsto \pmb {\rm { 750 \: m = 4\ell - 10 \: m} }$

$\longmapsto \pmb {\rm { 750 +10 \: m = 4\ell \: m} }$

$\longmapsto \pmb {\rm { 760\: m = 4\ell \: m} }$

$\longmapsto \pmb {\rm {\dfrac{ 760}{4}\: m = \ell \: m} }$

$\longmapsto \pmb {\rm { 190 \: m = \ell \: m} }$

$\longmapsto \pmb {\rm \red { 190 \: m = \ell ength} }$

Now, let's calculate its breadth.

From equation (i) , we have :

$\pmb {\rm {\mapsto b = \ell - 5 } }$

$\pmb {\rm {\mapsto b = 190 - 5 \: m} }$

$\pmb {\rm {\mapsto b = 185 \: m} }$

$\mapsto \pmb {\rm \red { 185 \: m = breadth} }$

Therefore,

• Length is 190 m.
• Breadth is 185 m.